CUET Mathematics Algebra > Linear Programming PYQs

Which of the following terms are associated with a linear programming problem? (A) Constraints (B) Independent events (C) Feasible region (D) Objective function Choose the correct answer from the options given below:

If $z = 3x + 4y$ be the objective function of a of a linear programming problem (LPP) and (3, 1), (2, 4), (0, 4), (5, 0) be corner points of the bounded feasible region. Then the maximum value of objective function is

The region represented by the system of inequalities $x, y \geq 0, y \leq 6, x + y \leq 3$

The corner points of the feasible region of a LPP with the constraints $x + 2y \leq 40$, $3x + y \geq 30$, $4x + 3y \geq 60$, $x, y \geq 0$ are

The corner points of the bounded feasible region determined by the system of linear constraints are $(0,8)$, $(4,4)$, $(12,12)$, $(0,20)$. Let $z = px + qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the maximum of $z$ occurs at both the points $(12,12)$, $(0,20)$ is

The point which provides the optimal solution of the linear programming problem maximize $z = 21x + 35y$ $3x + 2y \leq 30$ $4x + 5y \leq 60$ $x \geq 0, y \geq 0$ has the coordinates

If the feasible region of an LPP is bounded and the corresponding objective function is $z = 5x - 9y$, then the objective function attains:

The corner points of a bounded feasible region are (0, 5), (6, 1), (17, 2) and (4, 29). If the maximum value of objective function $z = px + qy$ where $p$ and $q > 0$ occurs at two points (17, 2) and (4, 29), then the relation between $p$ and $q$ is:

The sum of the x-coordinates of the corner points of the feasible region for the LPP: Minimize $z = 3x + 2y$ subject to constraints $x + y \leq 14$, $x \geq 4$, $x \leq 8, y \geq 0$ is

The objective function of an LPP is $z = ax + \beta y, (a, \beta > 0)$ in that has to be maximized/minimized subject to constraints $x + y \leq 2$, $x \geq 0$, $y \geq 0$. Then max (z) $-$ min (z) is equal to

As per the below-mentioned graph of shaded bounded feasible region of the LPP, the maximum value of the objective function $z = 2x + y$ is <img src="https://balti.afterboards.in/2vhvDBCiMgfU1Wc" width="400px"/>

A Linear Programming Problem (LPP) consists of which of the following components? (A) Decision variables (B) The graphical compliment (C) The objective function (D) The linear constraints Choose the **correct** answer from the options given below:

Consider an LPP: Maximise $Z = 50x + 15y$ subjected to constraints $x + y \leq 60$, $5x + y \leq 100$, $x, y \geq 0$. If the maximum value of $Z$ occurs at $x = \alpha$ and $y = \beta$, then the value of $\alpha + \beta$ is

Linear inequalities corresponding to the shaded feasible region OABCO in the given figure are <img src="https://balti.afterboards.in/XDcoYd2BxodBB7e" width="300px"/>

The feasible region corresponding to the linear constraints of a Linear Programming Problem (LPP) is represented by the shaded region in the given figure. Which of the following is not a constraint to the given LPP? <img src="https://balti.afterboards.in/AaGbmDtdftDHD7T" width="300px"/>

The corner points of the bounded feasible region for an LLP are: (5, 5), (15, 15), (0, 20) and (0, 10). Let $z = 3x + 9y$ be the objective function. Then the value of $maximum(z) - minimum(z)$ is

For the linear programing problem, $Minimize(Z) = 60x + 30y$ subject to: $2x - y \geq -5; 3x + y \geq 3; 2x - 3y \leq 12; x, y \geq 0$ the optimal value of $z$ is

The maximum value of $z$ for the linear programing problem maximize $z = x + y$ subject to the constraints $x + 4y \leq 8, 2x + 3y \leq 12, 3x + y \leq 9, x \geq 0, y \geq 0$ is:

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are <img src="https://balti.afterboards.in/rW5MYEPvXEmTawA" width="300px"/>

For the L.P.P. Maximize z = 10x + 6y subjected to 3x + y ≤ 12, 2x + 5y ≤ 34, x, y ≥ 0. Then the feasible region represented by system of inequalities is

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let z = px + qy where p, q > 0. Then the condition on p and q so that the maximum value of z occurs at (15, 15) and (0, 20) is

The linear inequalities satisfying the shaded feasible region given in the figure are <img src="https://balti.afterboards.in/YzPceJq35bcjnXJ" width="300px"/> (A) $x \geq 0$, $y \geq 0$, $2x + y \geq 2$ (B) $x \geq 0$, $y \geq 0$, $2x + y \leq 2$ (C) $x \geq 0$, $y \geq 0$, $2x + y \geq 2$, $x + 2y \leq 8$, $x - y \leq 1$ (D) $x + 2y \geq 8$, $x - y \geq 1$ Choose the correct answer from the options given below:

In an LPP, the feasible region represented by the set off constraints $2x + 3y \leq 18$, $x + y \leq 10$, $x \geq 0$, $y \geq 0$ is <img src="https://balti.afterboards.in/MsDd5yO8dQQKuwR" width="300px"/>

The corner points of the bounded feasible region for an LPP are (0,4), (4,4), (6,6), (0,12). If the objective function is $Z = px + qy, p > 0, q > 0$, then the condition on p and q so that maximum of Z occurs at (6,6) and (0,12) is

The solution set of the linear constraints $x - 2y \geq 0, 2x - y \leq -4, x \geq 0$ and $y \geq 0$ is

The corner points of the bounded feasible region associated with the LPP: Maximize $Z=px+qy$, $p,q>0$ are $(0, 0)$, $(3.5, 0)$, $\left(\frac{112}{59}, \frac{135}{59}\right)$ and $(0, 3)$. If the optimum value of Z occurs at both $\left(\frac{112}{59}, \frac{135}{59}\right)$ and $(0, 3)$, then

A person can sell a maximum of 20 units of shirts and pants on which a profit of ₹40 is made on each shirt and a profit of ₹30 on each pant. A minimum of 2 shirts are being sold, while pants are sold at least 4 times as many as shirts. Then the maximum profit is:

Which one of the following set of constraints represents the shaded region given below? <img src="https://balti.afterboards.in/D5IFnjn6aDlWkeZ" width="300px"/>

If the corner points of the bounded feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5), then the minimum value of objective function F = 4x + 6y occurs at

The corner points of the bounded feasible region for an LPP are (0, 20), (3,12), (6,8), and (0,15). The objective function is $Z = \alpha x + \beta y$, where $\alpha, \beta > 0$. If the maximum of Z occurs at the corner points (3,12) and (6,8), then the relationship between $\alpha$ and $\beta$ is:

The maximum value of a LPP $z = 3x + 4y$ subject to the constraints: $x + y \leq 6$, $x \geq 0$, $y \geq 0$ is:

If $z = 5x + 8y$ is the objective function of a LPP and (0, 0), (3, 1), (2, 4), (0, 3), (5, 0) are corner points of the bounded feasible region, then the maximum value of the objective function is

The corner points of the feasible region with the constraints $x + y \leq 30$, $x + y \geq 15$, $y \leq 20$, $x \leq 15$ and $x$, $y \geq 0$ are

The feasible region of a LPP is bounded. The corresponding objective function is Z= 6x - 7y. Then objective function attains:

The feasible region of a linear programming problem is bounded. The corresponding objective function is Z= 3x-4y. The objective function attains

The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is <img src="https://balti.afterboards.in/c8gWPn1f5aoJ3KP" width="300px"/>

The feasible region represented by the constraints: $x + 2y \geq 100$, $2x - y \leq 0$, $2x + y \leq 200$, $x \geq 0$, $y \geq 0$ of an LPP is: <img src="https://balti.afterboards.in/uiW8X6FYeOPBw6q" width="300px"/>

The corner points of the bounded feasible region determined by the system of linear constraints are (15,0), (40,0), (4,18) and (6, 12). If objective function is Z = 30x + 20y, then the sum of the maximum and the minimum values of Z is

The corner points of the bounded feasible region determined by a set of constraints in an LPP are $P(0, 5)$, $Q(3, 5)$, $R(5, 0)$ and $S(4, 1)$. If the objective function is $z = ax + 2by$, where, $a, b > 0$, then the condition on $a$ and $b$ such that the maximum value of $z$ occurs at $Q$ and $S$ is

For the LPP: minimize $z = 6x + 3y$ subject to the constraints $4x + y \geq 80$ $x + 5y \geq 115$ $3x + 2y \leq 150$ $x \geq 0, y \geq 0$ then the minimum value of z is

Match List-I with List-II | List-I | List-II | |---|---| | (A) Corner point of a feasible region | (I) The line segment joining any two arbitrary points of the region always lies entirely within the region | | (B) Bounded feasible region | (II) can not be enclosed within a circle | | (C) Unbounded feasible region | (III) can be enclosed within a circle | | (D) Convex region | (IV) Is a point of intersection of two boundary lines in the feasible region | Choose the correct answer from the options given below:

For the objective function $Z = 3x + 5y$ subject to constraints $x + 3y \geq 3$, $x + y \geq 2$, $x \geq 0$, $y \geq 0$:

If the objective function z = 4x + 3y has maximum value on a line joining points (3, a) and (b, 2) where a > 0, b > 0 such that a - b = 2, then the maximum value of z is:

With respect to the following shaded feasible region (ABCDEFA), the maximum value of the objective function z = 3x + 4y – 2 is at point(s): <img src="https://balti.afterboards.in/gUAK5hc16W6wryv" width="300px"/>

The corner points of a bounded feasible region determined by the following system of linear inequalities $x + 3y \leq 60, x + y \geq 10$, $x \leq y$, $x \geq 0$, $y \geq 0$ are (0,10), (5,5), (15, 15) and (0, 20). Let $z = 2px + qy$, $p, q > 0$. If maximum of z occurs at both (15, 15) and (0, 20), then the relation between p and q is

The corner points of the bounded feasible region of the LPP: Maximize $z = x + y$ subject to constraints $2x + 5y \leq 100$, $8x + 5y \leq 200$, $x \geq 0$, $y \geq 0$ are

If the corner points of bounded feasible region for an LPP are (0,2) (3,0) (6,0) (6,8) and (0, 5) then the minimum value of the objective function f=4x+6y occur at

For the objective function Z=-4x + 6y subject to the constraints 3x + 2y ≥ 5, 7x + 2y ≤ 9, x ≥ 0, y ≥ 0, the maximum value of Z occurs at $(a, b)$ and the minimum value of Z occurs at $(p, q)$ then the value of $\frac{a}{p} + \frac{b}{q}$ is:

For LPP: Maximize $z = 2x + 3y$ subject to the constraints $x + y \geq 2$, $x + 2y \geq 3$, $x \geq 0$, $y \geq 0$, which of the following graph represents the feasible region of the above LPP as shaded portion?

Consider the LPP: Maximize $z = 5x + 3y$ subject to $3x + 5y \leq 15$, $5x + 2y \leq 10$, $x,y \geq 0$. The optimal feasible solution occurs at

If the minimum value of the objective function $Z = ax + by$ of an LPP occurs at two points $(3, 5)$ and $(5, 3)$, then

From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function $z = 1.50x + 1.00y$; the maximum value of $z$ will be: <img src="https://balti.afterboards.in/TZVsJcDnM85gOPS" width="300px"/>

The maximum value of the objective function $z = 10x + 15y$ of an L.P.P. subjected to the constraints $2x + 4y \leq 8$, $3x + y \leq 6$, $-x - y \geq -4$, $x \geq 0$, $y \geq 0$ is:

The minimum value of $Z = 2x + y$ subjected to $x + y \geq 10, 2x + 3y \leq 26, x, y \geq 0$ is

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0,0)$, $(4,0)$, $(2,4)$ and $(0,5)$. If maximum value of $z = ax + by$, where $a,b > 0$, occurs at both $(2,4)$ and $(4,0)$ then

The corner points of the feasible region determined by a system of linear constraints are $(0, 0)$, $(0, 40)$, $(20, 40)$, $(60, 20)$, $(60, 0)$. If the objective function is $z = 4x + 3y$, then which one of the following is true?

Consider the LPP: Max $Z = 5x + 3y$ subject to $3x + 5y \leq 15, 5x + 2y \leq 10, x \geq 0, y \geq 0$ Match **List-I** with **List-II** | List-I | List-II | |---|---| | (A) Objective function | (I) $3x + 5y \geq 15$ | | (B) One constraint | (II) $x, y \geq 0$ | | (C) Non-negative restrictions | (III) $Z = 5x + 3y$ | | (D) Point $(1, 2)$ does not lie in the region | (IV) $3x + 5y \leq 15$ | Choose the correct answer from the options given below:

The minimum value of $z = 3x + 2y$ subjected to the constraints $2x + y \geq 7, x + 2y \geq 8, x, y \geq 0$ is

Which one of the following represents the correct feasible region determined by the following constraints $x - y \geq 5$, $5x - 5y \leq 16$

The maximum value of $z = 5x + 7y$ subjected to constraints $x + y \leq 5$, $x \geq 0$, $y \geq 0$ is:

Which of the region shown in the given figures represents the feasible region bounded by the following constraints? $4x + y \geq 80$, $2x + y \geq 60$, $x + y \leq 80$, $x \geq 0$, $y \geq 0$ <img src="https://balti.afterboards.in/amdVa7RhS90gsFU" width="300px"/>

The corner points of the bounded feasible region determined by the system of linear constraints are $(0, 0)$, $(5, 0)$, $(6, 5)$, $(6, 8)$, $(4, 10)$, $(0, 8)$. Let $Z = 3x - 4y$ be the objective function. The minimum value of Z occurs at

For the linear programming problem (LPP): Maximize $Z = x + 1.5y$, subject to constraints, $x + 2y \leq 40$, $2x + y \leq 40$, $x + y \leq 25$, $x \geq 0$, $y \geq 0$. Which of the following is NOT correct?

About linear programming problem (LPP), which of the following statements are correct? (A) In a LPP, the linear inequalities or restrictions on the variables are called linear constraints. (B) If the feasible region for an LPP is unbounded, then the maximum or minimum value of the objective function $Z = ax + by$ never exists. (C) The feasible region for an LPP is always convex. (D) The common region determined by all the linear constraints of an LPP is called the feasible region. Choose the correct answer from the options given below:

If the objective function $z = px + qy$ has its maximum value at the points (2, 1) and (0, 6), then the relationship between p and q is:

The corner points of the bounded feasible region determined by the system of linear constraints are $(0, 0), (5, 0), (6, 5), (6, 8), (4, 10), (0,8)$. Let $z = 3x - 4y$ be the objective function. Then the minimum value of the objective function z occurs at

The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (5, 0), (3, 4) and (0, 5). Let $Z = px + qy$ where $p, q > 0$. Condition on p and q so that the maximum of Z occurs at both (5, 0) and (3, 4) is

Consider a L.P.P, Maximize $Z = 3x + 5y$ subject to constraints $2x + 6y ≤ 6$, $x - y ≥ 0$, $x ≥ 0$, $y ≥ 0$. Then which of the following are true? (A) The feasible region of L.P.P is bounded region (B) The corner points of the feasible region are (0, 0), (2, 2), (0, 1) (C) Maximum value of Z is 9 (D) Point (1, 3) lies in the feasible region Choose the correct answer from the options given below:

In a linear programming problem(LPP), the maximum value of the objective function $Z = 2x + 5y$ subjected to the constraints: $2x + 3y ≤ 6$ $2x + y ≤ 4$ $x, y ≥ 0$ is

Which of the following are correct about the linear programming problem(LPP)? (A) The objective function is always linear. (B) A corner point of a feasible region is a point in the region which is the intersection of two boundary lines. (C) The common region determined by all the linear constraints of a LPP is called the feasible region. (D) If an LPP admits optimal solution at two points then its optimal values occurs at an infinite number of points. Choose the correct answer from the options given below:

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below? <img src="https://balti.afterboards.in/BMA5vBPSyJrH2hF" width="300px"/>

Consider the Linear Programming Problem Maximize $z = x + y$ Subject to the constraints $x - y \leq -1$, $x \geq y$, $x \geq 0, y \geq 0$ Then which one of the following is TRUE?

In a linear programming problem, the constraints on decision variables $x$ and $y$ are $y-2x \leq 0$, $y \geq 0$, $0 \leq x \leq 5$. The feasible region of the above problem:

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0, 0)$, $(2, 4)$, $(0, 5)$ and $(4, 0)$. If the maximum value of $z = ax + by$, where $a, b > 0$ occurs at both $(2, 4)$ and $(4, 0)$, then

A furniture trader deals in only two items - chairs and tables. He has Rs. 50,000 to invest and a space to store almost 35 items. A chair costs him Rs. 1000 and a table costs him Rs. 2000. The trader earns a profit of Rs. 150 and Rs. 250 on a chair and a table, respectively. Choose the correct option among following that describes the given linear programming problem (LPP) to maximize the profit ( where x and y are the number of chairs and tables that trader buys and sells)?

If the corner points of the bounded feasible region for a Linear Programming Problem (LPP) are A(0,2), B(3, 0), C(2, 3) and D(3, 1), then the maximum value of the objective function $Z = 4x + 2y$ occurs at

The corner points of the bounded feasible region determined by a set of constraints (linear inequalities) are A(0, 5), B(3, 5), C(5, 0) and D(4, 1) and the objective function is z = $px$ + 2$qy$ where p,q > 0. The condition on $p$ and $q$ such that the maximum z occurs at B and D, is:

Consider the following L.P.P. Minimize z = 400x + 300y subject to 100x + 200y ≥ 12000, 300x + 400y ≥ 20000, 200x + 100y ≥ 15000 and x, y ≥ 0. Then

Consider the following L.P.P Max. z = 5x + 2y; subject to -2x - 3y ≤ -6, x - 2y ≤ 2, 3x + 2y ≤ 12, -3x + 2y ≤ 3 and x, y ≥ 0 then

Consider the following L.L.P. Minimize z = 30x - 30y + 1800; subject to x + y ≤ 30, x ≤ 15, y ≤ 20, x + y ≥ 15 and x, y ≥ 0. Then it attains its optimal value at the point

The corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 3/2), (1, 2) and (4, 0). If the objective function is Z = ax + by, where 'a' and 'b' are positive, then the condition on 'a' and 'b' so that the maximum of Z occurs at (1, 2) and (4, 0) is:

Consider the linear programming problem (LPP): Maximize Z = 6x + 3y subject to the conditions, 4x + y ≥ 80, x + 5y ≥ 115, 3x + 2y ≤ 150, x, y ≥ 0. In reference to the above LPP, which of the following are correct? (A) The feasible region is bounded. (B) The corner points of the feasible region are (15, 20), (40, 15) and (0, 75). (C) The maximum value of the objective function is 285. (D) The LPP does not have optimal solution. Choose the correct answer from the options given below:

The feasible region represented by the constraints $x + y \leq 50, 3x + y \leq 90, x \geq 0, y \geq 0$ of an LPP is <img src="https://balti.afterboards.in/PT2fmLOw2WWECQ6" width="300px"/>

For the given linear programming problem $z = ax + by; a, b > 0$ subject to the constraints $2x + y \leq 10, x + 3y \leq 15, x, y \geq 0$. If the corner points are (0,0), (5,0), (3,4) and (0,5) and z is maximum at both (3,4) and (0,5), then the relationship between a and b is

An objective function $z = ax + by$ is maximum at points (15,15) and (0, 20). If $a, b \geq 0$ and $ab = 27$, then the maximum value of the objective function is

Consider the following L.P.P minimize $z = x - 7y + 190$ subject to $x + y \le 8, x + y \ge 4, x \le 5, y \le 5$ and $x, y \ge 0$. Then which of the following is/are true? (A) It's feasible region is unbounded (B) It's feasible region is bounded (C) It's feasible region has 5 corner points (D) It's feasible region has 6 corner points Choose the **correct** answer from the options given below:

If the corner points of the bounded feasible region for a linear programming problem (LPP) are (0, 2), (3, 0), (6, 0), (6, 8) and (0,5), then which of the following are correct for the objective function $Z = 4x + 6y$? (A) The minimum value of the objective function occurs at (0, 2) and (3, 0) only. (B) The minimum value of the objective function occurs at the mid-point of the line segment joining the points (0, 2) and (3, 0) only. (C) The minimum value of the objective function occurs at every point of the line segment joining the points (0, 2) and (3, 0). (D) The difference between the maximum value and minimum value of the objective function is 60. Choose the correct answer from the options given below:

If the objective function for a linear programming problem (LPP) is $Z = 4x + 5y$ and the corner points of the bounded feasible region are (9, 0), (4, 3), (2, 5), and (0,8), then the minimum value of Z is:

If the optimal value of the objective function $z = px + y$ of an L.P.P occurs at two corner points (2, 11) and (4, 5) of its bounded feasible region, then its optimal value is

The constraints of the given shaded feasible region below of an L.P.P., for non-negative variable constraints $x$ and $y$ are <img src="https://balti.afterboards.in/IECuq9aGxsHDLdW" width="300px"/>

A linear programming problem is as follows: Minimize $z = 2x + 3y$ Subject to the constraints $x \ge 3, x \le 9, y \ge 0, x - y \ge 0, x + y \le 14$. The feasible region has 5 corner points including

The maximum value of the objective function $z = 2x + 3y$ of an L.P.P. subjected to the constraints $x - y \le 1$, $x + y \le 3$, $x, y \ge 0$ is

Let the corner points of the bounded feasible region of the linear programming problem (LPP) $Z = ax+by$ be: (0, 0), (2, 0), (20/19, 45/19) and (0, 3). If the optimal value of Z occurs at both points (2, 0) and (20/19, 45/19), then the relation between a and b is:

For the linear programming problem (LPP), $Maximize Z = 7x + 9y$, subject to constraints, $x - y \le -1, -x + y \le 0, x, y \ge 0.$ Which of the following is correct?

The region represented by the constraints $x \geq 0, y \geq 0$ of an LPP is

The maximum value of the objective function $Z = 8x + 2y$ of an LPP subject to constraints $2x + y \leq 3, 2x + 3y \leq 6, x \geq 0, y \geq 0$ is:

The minimum value of the objective function $z = x + 2y$ of an L.P.P. subject to constraints $2x + y \geq 3, \frac {x} {2} + 2y \geq 6, x \geq 0, y \geq 0$ is:

For an LPP: Maximize $z = 3x + 9y$, $x \geq 0, y \geq 0$, the feasible region OAB is shown in the figure, then the other constraints are <img src="https://balti.afterboards.in/HfoMd9Ve3v1q1ag" width="400px"/>

The maximum value of the objective function $Z = 2x + y$ of an LPP, subject to the constraints $x \leq 6, y \leq 2, x - y \leq 0$, $x \geq 0, y \geq 0$ is

If the objective function $Z = px + qy, p > 0, q > 0$ of a linear programming problem attains its optimal value at the points (4, 7) and (5, 5) and $pq = 50$ then

Consider the linear programming problem(LPP): *Minimize* $Z = x + y$ $x + 2y \leq 4,$ $3x + y \geq 3,$ $4x + 3y \geq 6,$ $x, y \geq 0.$ Which of the following is correct for the above linear programming problem (LPP): (A) The LPP has a bounded feasible region. (B) The LPP has a unique optimal solution. (C) The optimal value of the LPP exists at the point (3/2, 0) (D) The corner points of the feasible region are (3/2, 0), (3/5, 6/5), (2/5, 6/5) and (4, 0) Choose the **correct** answer from the options given below:

The corner points of the feasible region associated with the LPP: Maximise $Z = px + qy$, $p,q > 0$ subject to $2x + y \leq 10$, $x + 3y \leq 15$, $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then

Consider the LPP: Minimize $Z = x + 2y$ subject to $2x + y \geq 3$, $x + 2y \geq 6$, $x, y \geq 0$. The optimal feasible solution occurs at

Which one of the following set of constraints does the given shaded region represent? <img src="https://balti.afterboards.in/0PPxlbCRpdvsuFO" width="400px"/>

The corner points of the feasible region of the LPP: Minimize $Z = -50x + 20y$ subject to $2x - y \geq -5$, $3x + y \geq 3$, $2x - 3y \leq 12$ and $x, y \geq 0$ are

Which of the following is NOT a basic requirement of the linear programming problem (LPP)?

Which of the following statements are correct in reference to the linear programming problem(LPP): Maximize ${Z} = 5x + 2y$ subject to the following constraints $3x + 5y \leq 15$, $5x + 2y \leq 10$, $x \geq 0, y \geq 0$. (A) The LPP has a unique optimal solution at $(2, 0)$ only. (B) The feasible region is bounded with corner points $(0, 0)$, $(2, 0)$, $(20/19, 45/19)$ and $(0, 3)$. (C) The optimal value is unique, but there are an infinite number of optimal solutions. (D) The feasible region is unbounded. Choose the correct answer from the options given below:

The objective function of an LPP is $z = ax + by$. If the maximum value of the objective function is 180, which occurs at two points (15,15) and (0,20), then which one of the following is true?

If the corner points of the bounded feasible region of an LPP with objective function Maximize $z = 2x + 3y$ are (0,0), (1,2) and (1,1), then its optimal value is

The feasible region of the linear programming problem is represented below: <img src="https://balti.afterboards.in/2p1sfNGWOxx6GJZ" width="400px"/> The constraints of this LPP are

The optimal value of the objective function of the LPP, Minimize $Z = 3x - 2y$ subject to constraints $x + y \ge 10$, $3x + 5y \ge 15$, $x \ge 0$, $y \ge 0$, is equal to:

Which of the following is incorrect about the Linear Programming Problem (LPP)?

A manufacturing unit makes two models, 'classic' and 'supreme' of the scooter. Each piece of the classic model requires 9 labour hours for assembling and 1 labour hour for finishing. Each piece of supreme model requires 12 labour hours for assembling and 3 labour hour for finishing. For assembling and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of ₹ 10000 on each piece of the classic model and ₹ 15000 on each piece of the supreme model. Which of the following options describes the given Linear Programming Problem (LPP) to maximize the profit Z (Max Z) (where x and y are the number of pieces of the classic model and the supreme model respectively)?

If corner points of the bounded feasible region are (0, 0), (3, 0) and (0, 3) and objective function is $z = 4x + 7y$, then the maximum value of $z$ is

In the given figure, feasible region represented by the constraints $4x + y \geq 80$, $x + 5y \geq 115$, $3x + 2y \leq 150$, $x,y \geq 0$ is <img src="https://balti.afterboards.in/Q5P6ZSbdDi1Plzz" width="400px"/>

The feasible region associated with the inequality $2x + 3y > 4$ is

Consider the LPP: Maximize $z = x + y$ subject to the constraints $x + 2y \leq 70$, $2x + y \leq 95$, $x,y \geq 0$. The optimal feasible solution is

For the linear programming problem(LPP), Maximize $Z = 4x + y$ $x + y \leq 5$ $3x + y \leq 9$ $x,y \geq 0$. Which of the following are NOT true? (A) The given LPP has unbounded feasible region. (B) The corner points of the feasible region are (0,0), (0, 5), (3, 2) and (3, 0). (C) The optimal value of the objective function is 12. (D) The given LPP has a unique optimal solution. Choose the correct answer from the options given below:

If a person rides his motorbike $x$ km at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol. If he rides $y$ km at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is:

The corner points of the feasible region determined by $x+y \leq 8, 2 x+y \geq 8, x \geq 0, y \geq 0$ are $A(0,8), B(4,0)$ and $C(8,0)$. If the objective function $Z=a x+$ by has its maximum value on the line segment $A B$, then the relation between $a$ and $b$ is :

An objective function $Z=a x+b y$ is maximum at points $(8,2)$ and $(4,6)$. If $a \geq 0$ and $b \geq 0$ and $a b=25$, then the maximum value of the function is equal to :

<img src="https://balti.afterboards.in/QKMiqcaA8YsIhak" width="500px"/> The feasible region represented by the constraints $4 x+y \geq 80, x+5 y \geq 115,3 x+2 y \leq 150, x, y \geq 0$ of an LPP is

Which one of the following represents the correct feasible region determined by the following constraints of an LPP? $x+y \geq 10,2 x+2 y \leq 25, x \geq 0, y \geq 0$

A person wants to invest an amount of ₹ $75,000$. He has two options A and B yielding $8 \%$ and $9 \%$ return respectively on the invested amount. He plans to invest at least ₹ $15,000$ in Plan A and at least ₹ $25,000$ in Plan B. Also he wants that his investment in Plan A is less than or equal to his investment in Plan B. Which of the following options describes the given LPP to maximize the return (where $x$ and $y$ are investments in Plan A and Plan B respectively) ?

The corner points of the feasible region for an L.P.P. are $(0,10),(5,5),(5,15)$ and $(0,30)$. If the objective function is $Z=\alpha x+\beta y, \alpha, \beta>0$, the condition on $\alpha$ and $\beta$ so that maximum of $Z$ occurs at corner points $(5,5)$ and $(0,20)$ is :

If $5x + y \leq 100$, $x + y \leq 60$, $x \geq 0$, $y \geq 0$. Then one of the corner points of the feasible region is :

In a LPP, let R be the feasible region. A. If R is unbounded then a max./min. value of objective function may not exist. B. If R is bounded then a max. and min. value of objective function will always exist. C. If a solution exists, it must occur at a corner point. D. If R is bounded then max. will exist but min. may or may not exist for an objective function. Choose the correct answer from the options given below:

A manufacturing company makes two models M$_1$ and M$_2$ of a product. Each piece of M$_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of M$_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs.800 on each piece of M$_1$ and Rs.1200 on each piece of M$_2$ The above Linear Programming Problem [LPP] is given by

A manufacturing company makes two models M$_1$ and M$_2$ of a product. Each piece of M$_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of M$_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs.800 on each piece of M$_1$ and Rs.1200 on each piece of M$_2$ The maximum profit will be at the point

The feasible region for an LPP is shown below. Let $Z = 3x - 4y$ be the objective function. Maximum of Z occurs at : <img src="https://balti.afterboards.in/P4A0ckrzsn6mVTf" width="300px"/>

The region represented by the system of inequalities $x, y \geq 0$ ; $2x + 3y \geq 4$ ; $x \geq 1$ is :

Owner of a whole sale computers shop plans to sell 2 types of computers. A desktop and portable model. If $x$ is the number of desktops and $y$ is the number of portable model and the shop's capacity cannot exceed 250 units. Which of the following is correct ?

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ is :<img src="https://balti.afterboards.in/fjQTz13IBfFlQGM" width="400px"/>

In a Linear Programming problem, the objective function is always :

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is $z = 4x + 3y$. Compare the quantity in Column - A and Column - B. | Column - A | Column - B | |---|---| | Maximum value of z | 350 |

The corner points of the feasible region determined by the following system of linear inequalities : $2x + y \leq 10$, $x + 3y \leq 15$, $x, y \geq 0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let $z = px + qy$, where $p, q > 0$ condition on p and q so that maximum of z occurs at both (3, 4) and (0, 5) is :

For the LPP Maximise $z = x + y$ subject to $x - y \leq -1$, $-x + y \leq 2$, $x, y \geq 0$, $z$ has :

Choose the wrong statement from the following :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) The common region determined by all the constraints of LPP is called | (I) objective function | | (B) Minimize $z = c_1x_1 + c_2x_2 + ..... + c_nx_n$ is | (II) convex set | | (C) A solution that also satisfies the non-negative restrictions of a LPP is called | (III) feasible region | | (D) The set of all feasible solutions of a LPP is a | (IV) feasible solution | Choose the correct answer from the options given below :

If corner points of a feasible region are (0, 0), (2, 0), $\left(\frac{20}{19}, \frac{45}{19}\right)$ and (0, 3), then (A) Maximum value of $z = 5x + 3y$ is 10 (B) Minimum value of $z = 5x + 3y$ is 0 (C) Maximum value of $z = 5x + 3y$ is $\frac{235}{19}$ and minimum value is 0 (D) Maximum value of $z = 5x + 3y$ is 10 and minimum value is 0 Choose the correct answer from the options given below :

The solution of LPP max.(z) = $5x + 3y$ subject to $2x + y \leq 6$ $x + y \leq 4$ $x \geq 0, y \geq 0$, is

The corner points of the feasible region determined by inequalities of LPP are $(4, 10)$, $(6, 8)$ and $(6, 5)$. Let $z = 3x + 4y$ be the objective function. Then the sum of maximum value of z and minimum value of z is :

Consider the linear programming problem : Minimize $z = 50x + 70y$ Subject to $2x+y \geq 8$, $x+2y \geq 10$, $x \geq 0$, $y \geq 0$ The minimum value of objective function is :

The optimal solution of the Linear Programming problem Maximize $Z = 3x_1 + 5x_2$, s.t. $3x_1 + 2x_2 \leq 18$ $x_1 \leq 4$ $x_2 \leq 6$ $x_1 \geq 0, x_2 \geq 0$ is

The optimal value of linear programming problem maximum $Z = 3x + 4y$, subject to, $x + 3y \leq 12$ $x + y \geq 8$ $x, y \geq 0$ is

The objective function for a L.P.P. is $Z = 5x + 7y$ and the corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4) and (0, 2), then the maximum value of Z occurs at

The maximum value of $z = 4x + 3y$, if the feasible region for an LPP is as shown below is:<img src="https://balti.afterboards.in/yaqRTNOpRch3l7q" width="400px"/>

A manufacturer of electronic circuit has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs. 50 and that on type B circuit is Rs. 60, identify the constraints for this LPP, if it was assumed that x circuit B of type A and y circuits of type B was produced by the manufacturer. A. $x + 2y \geq 15$ B. $2x + y \leq 20$ C. $x + 2y \leq 12$ D. $x, y \leq 0$ Choose the correct answer from the options given below

The vertices of a closed convex polygon representing the feasible region of the LPP with, objective function $z = 5x + 3y$ are $(0, 0)$, $(3, 1)$, $(1, 3)$ and $(0, 2)$. The maximum value of $z$ is

In linear programming, the optimal value of the objective function is attained at the points given by

The corner points of the feasible region for an L.P.P. are $(0, 10)$, $(5, 5)$, $(15, 15)$ and $(0, 20)$. If the objective function is $z = px + qy$; $p, q > 0$, then the condition on $p$ and $q$ so that the maximum of $z$ occurs at $(15, 15)$ and $(0, 20)$ is

If the objective function for an LPP is max.$(z) = 300x + 700y$ and the corner points for the bounded feasible region are $(6,0)$ $(5,0)$ $(0,6)$ $(4,4)$ and $(0,4)$, then the maximum values of z occurs at :

The feasible region and optimal solution of a LPP with objective function, max.$(z) = 600x + 400y$, subject to : $x + 2y \leq 12$, $2x + y \leq 12$, $x + 1.25y \geq 5$, $x \geq 0$ and $y \geq 0$, is:<img src="https://balti.afterboards.in/qaJVYwB0zdE2O4c" width="400px"/> The feasible region and optimal solution is _____

The programming problem Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

The solution of a LPP with basic feasible solutions (0, 0), (10, 0), (0, 20), (10, 15) and objective function Max $Z = 2x + 3y$ is :

The linear constraints, for which the shaded area in the figure is the feasible region of an LPP, are :<img src="https://balti.afterboards.in/uuDFz7SlhIgJEH7" width="400px"/>

The feasible region of an LPP Max $Z = 3x + 2y$ subject to $x \geq 0, y \geq 0, x - 2y \leq 3$ is: