CUET Mathematics Applied Mathematics > Linear Programming PYQs

The bounded feasible region of an LPP is shown in the diagram given below. The objective function $z=3x+10y$ attains optimum values at : <img src="https://balti.afterboards.in/gJcms7Bb2ql0aVM" width="400px"/> A. Point (0,0) B. Point (0,4) C. Point (6,3) D. Point (5,6) Choose the correct answer from the options given below:

Every gram of wheat provides 0.15 g of proteins and 0.24 g of carbo hydrates. The corresponding values of proteins and carbo hydrate of rice are 0.05g and 0.48g respectively. Wheat costs ₹40 per kg and rice costs ₹60 per kg. The minimum daily requirements of proteins and carbohydrates for an average child are 50g and 200 g respectively. Which of the following options describes the LPP to minimize the total cost of wheat and rice that provide minimum daily requirements of proteins and carbohydrates ?

Match the LIST-I with LIST-II | | LIST-I | | LIST-II | |---|---|---|---| | A. | In a L.P.P the objective function is always | I. | Finite | | B. | Feasible region for an L.P.P is always a | II. | Convex set | | C. | In an L.P.P having bounded feasible region, the maximum value of the objective function $z = ax + by$ is always | III. | Linear | | D. | Feasible region is the set of points which satisfy | IV. | All the given constraints | Choose the correct answer from the options given below:

If the objective function $z=10(x-7y+190)$ and the corner points of the bounded feasible region are A(0,4), B(0,5), C(3,5), D(5,3), E(5,0), F(4,0), then the minimum value of z will be:

Objective function $Z = 200x + 500y$, subject to constraint, $x + 2y \geq 10, 3x + 4y \leq 24$, $x \geq 0, y \geq 0$ - (iii), the minimum value of Z is :

Given a linear programming problem, Max $Z = 22x + 18y$, Subject to constraints $x + y \leq 20, 360x + 240y \leq 5760, x \geq 0, y \geq 0$. Its corner points are :

The corner points of feasible region determined by the following system of linear inequalities $2x + y \leq 10, x + 3y \leq 15, x \geq 0, y \geq 0$ are $(0,0), (5,0), (3,4)$ and $(0,5)$, then the relation between p and Q so that minimum of Z occurs both points $(3,4)$ and $(0,5)$ is :

For the LPP, Min $Z = 6x + 10y$ subject to $x \geq 6, y \geq 3, 2x + y \geq 10, x \geq 0, y \geq 0$, redundant constraint is :

Which of the following is a correct set of constraint for a LPP ?

For the feasible reason of a LPP as shown, if the equation of OA and BC are $y - 2x = 0$ and $y - 2x = 4$ respectively than constraints for LPP are

Objective function of a LPP represent

Which constraints correctly represent the situation 'mixture of x and y must be at least 8 units' ?

The feasible reason for the constraints $x \geq 0$, $x + y \leq 1$ and $x - y \leq 1$, is situated in : (A) I and II quadrant only (B) I Quadrant (C) II and IV Quadrant (D) IV Quadrant (E) I , II , III and IV Quadrant Choose the correct answer from the option given below :

Value of Z equals to 40x + 50y subject to constraints $3x + y \leq 9$, $x + 2y \leq 8$, $x, y \geq 0$ occurs at

The corner point of the feasible region determined by a set of linear constraints are : (0,0) , (0,4), (2,5) , (6,3) and (6,0) then which of the following point lie in the feasible region ?

A company produces two types of belts A & B with a profit of Rs 2 and Rs 1.50 respectively. Belt of type A needs twice as much time to make as belt type B . The company can produce at the most 1000 belts of type B per day . Material for 800 belts is available per day . At the most , 400 buckles for belt type A and 700 for belts type B are available . Then the appropriate LPP is :

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

The Solution set of the inequality three $3x + 4y \leq 12$ is :

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let $Z = ax + by$, where a, b > 0. Condition on a and b so that the maximizing value of Z occurs at both the points (15, 15) and (0, 20) is:

The feasible region for an LPP is shown in the figure given below: If objective is maximizing $Z = 22x + 18y$ find $(x, y)$ for the optimal $Z$.<img src="https://balti.afterboards.in/uzsNn04Qzqljaui" width="400px"/>

If the objective function for an L.P.P. is $z = 3x + 4y$ and the corner points for unbounded feasible region are (9, 0), (4, 3), (2, 5) and (0, 8), then the minimum value of $z$ occurs at :

If objective function $Z = 20x + 30y$ of an LPP is subject to the constraints $3x + 4y \geq 12$, $4x + y \geq 4$, $x \geq 0, y \geq 0$, then Z has : (A) Min at (0, 4) (B) Max at (0, 4) (C) Min at (4, 0) (D) Max at (4, 0) (E) Min at $\left(\frac{4}{13}, \frac{36}{13}\right)$ Choose the **correct** answer from the options given below :

In an LPP if the objective function $z = ax + by$ has same maximum value on two corner points of the feasible region, then the number of points at which maximum value of $z$ occurs is :

Corner points of the feasible region for an LPP are : (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let $z = 4x + 6y$ be the objective function. Then, Max z $-$ Min z is equal to :

The objective function $z = 4x + 3y$ can be maximised subject to the constraints $3x + 4y \leq 24$, $8x + 6y \leq 48$, $x \leq 5$, $y \leq 6$, $x \geq 0$, $y \geq 0$ :

The maximum value of $Z = 3x + 4y$ subjected to the constraints $3x + 7y \leq 21$, $5x + 2y \leq 10$; $x, y \geq 0$ is :

The minimum value of $z = 3x + 6y$ subject to the constraints $2x + 3y \leq 180$, $x + y \geq 60$, $x \geq 3y$, $x \geq 0$, $y \geq 0$ is :

A carpenter earns a profit of ₹ 50 and ₹ 80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as : | Required | Chair | Table | Available quantity | |----------|-------|-------|--------------------| | Wood | 3 | 5 | 150 | | Labour | 1 | 2 | 56 | The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively :

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) The common region determined by all the linear constraints of a L.P.P. is called | (I) corner point | | (B) A point in the feasible region which is the intersection of two boundary lines is called, | (II) non-negative | | (C) The feasible region for an LPP is always a | (III) feasible region | | (D) The constraints $x, y \geq 0$ describes that the variables involved in a LPP are | (IV) convex polygon | Choose the correct answer from the options given below :

The maximum value of $Z = 3x + y$ subject to the constraints $x + y \leq 30, 2x + y \leq 40, x, y \geq 0$ is

Match List I with List II | LIST I | LIST II | |---|---| | A. A solution that does not satisfy all the constraints is called | I. Linear | | B. The objective function in an LPP is | II. Convex polygon | | C. Linear inequalities or equations on the variables of LPP are called | III. Infeasible solution | | D. The feasible region in an LPP, formed by the convex combinations of the corner points, is called | IV. Constraints | Choose the correct answer from the options given below:

The minimum value of $Z = 30x + 10y$ subject to the constraints $x + 2y \leq 30, 3x + y \geq 30, 4x + 3y \geq 60, x, y \geq 0$ is

If the objective function $Z = px + qy$ ($p, q > 0$) of an LPP has minimum value 7p, at the corner points (2, 3) and (7, 0), then