CUET Mathematics: AlgebraLinear Programming. Free, no login required.

Consider the objective function $Z = 3x + 4y$ subject to the following constraints: $x-6y \le 6, x+y-1 \ge 0, x-y+1 \ge 0, x+2y \le 6, x \ge 0, y \ge 0$ . Which of the following inequalities does not contribute to the feasible region?

A company makes two types of cakes: type A and type B. it costs ₹ 360 to make a type A cake and ₹ 120 to make a type B cake. The company can make atmost 300 cakes and spend atmost ₹ 72,000 a day, the number of cakes of type B ($y$) cannot exceed the number of type A ($x$) cakes by more than 200.

The company makes a profit of ₹ 200 on each type A cake and ₹ 50 on each type B cake. A LPP to maximize the profit (₹) is

The feasible region represented by the constraints $2x+y \le 12, x+2y \le 12, 4x+5y \ge 20, x,y \ge 0$ of LPP is

The corner points of the feasible region of a LPP are (0,2), (3,0), (6,0), (6,8) and (0,5). If the objective function is $z = 4x + 6y$, then the sum of maximum and minimum value of z is equal to:

Consider the LPP: Minimize $z=-50x+20y$ subject to $2x-y\ge -5, 3x+y\ge 3, 2x-3y\le 12, x\ge 0, y\ge 0$. Then which of the following statements are TRUE?

(A) Corner points of the feasible region of the LPP are (0,5), (0,3), (1,0), (6,0).

(B) The optimum value of the objective function is -300

(C) Optimum value does not exist

(D) The optimum value of the objective function is 100

Choose the correct answer from the options given below:

For the LPP,

$Z=20x+10y$

Subject to

$x+2y\le 40$

$3x+y\ge 30$

$4x+3y\ge 60$

$x,y\ge 0$

Match List-I with List-II

Choose the correct answer from the options given below:

In reference to linear programming problem (LPP), which of the following statement is NOT correct?

The corner points of the bounded feasible region determined by $x+3y\le60, x+y\ge10, x\le y, x\ge0, y\ge0$ are A(0, 10), B(5, 5), C(15, 15) and D(0, 20). If the objective function $z=ax+by$ has its maximum value on the line segment CD, then the relation between $a$ and $b$ is:

For a LPP, maximize $z=2x+3y$, subjected to constraints:

$x\ge2, x\le7, y\le x, x+y\le10, x\ge0, y\ge0$

Which of the following statements are TRUE ?

(A) Vertices of feasible region are (2, 0), (7, 0), (7, 3), (5, 5) and (2, 2).

(B) Maximum $z=25$ at point (5, 5).

(C) Maximum $z=25$ at infinite numbers of points.

(D) The feasible region is unbounded.

Choose the correct answer from the options given below:

The linear constraints for which the shaded region in the figure is the solution set, are

A manufacturer produces two products, A and B. Both products are processed on two different machines. The available capacity of the first machine is 12 hours and of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at ₹7 profit and that of product B at a profit of ₹4. A LPP to maximise the profit is:

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

Consider a LPP with objective function $z = ax + by$. If its feasible region R is bounded, then $z$

Consider a LPP with objective function $Z = px + qy$ subjected to certain constraints with a bounded feasible region such that maximum $Z = 80$ and minimum $Z = 52$, which occur at the corner points $(0, 8)$ and $(2, 4)$ respectively, Then the value of $p+q$ is:

Which one of the following set of constraints depicted the shaded region given below?

The corner points of the bounded feasible region for an LPP are $(0,5), (6,6), (9,9)$ and $(0,12)$. 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 $(9,9)$ and $(0,12)$ is

Consider an LPP:

Maximise $Z = 15x + 10y$

Subject to $2x + y \le 40$

$2x + 3y \le 80$

$x, y \ge 0$

Which of the following are correct?

A. The feasible region is bounded.

B. The corner points of the feasible region are $(0,0), (40,0), (10,20)$ and $(0,40)$.

C. The corner points of the feasible region are $(0,0), (20,0), (10,20)$ and $\left(0, \dfrac{80}{3}\right)$.

D. The maximum value of Z is 350.

Choose the correct answer from the options given below:

The feasible region for a LPP is shown in the figure. The minimum value of Z = 2x - 3y is

The maximum value of $z = 3x + 4y$ subject to the constraints

$x + y \geq 2, 2x + 3y \leq 6, x \geq 0, y \geq 0$ is

The number of corner points of the feasible region determined by the constraints $2x - y \geq 0, x - 3y + 3 \geq 0, x \geq 0, y \geq 0$ is

The feasible region of inequality $2x + 3y > 6$ is

Max (z) = 5x + 10y subject to constraints:

$x + 2y < 120$

$x + y > 60$

$x - 2y > 0$

$x, y \geq 0$

Which of the following points do not lie in the feasible region of the above LPP ?

(A) (90, 15)

(B) (30, 15)

(C) (60, 20)

(D) (90, 10)

Choose the correct answer from the options given below:

Refer to the LPP given by $Z = 2.5x + y$, subject to constraints

$3x + y \le 12; 3y + x \le 12; x, y \ge 0$:

In the given figure, If $Z_A$ = value of Z at A, $Z_C$ = value of Z at C and Max.(Z) = maximum value of Z, then which of the following relations between $Z_A$, $Z_C$ and Max.(Z) are correct?

A. $2Z_A = 5$ Max.(Z)

B. $5Z_A = 2Z_C$

C. $Z_A = 6 + Z_C$

D. $6+Z_A = Z_C$

Choose the correct answer from the options given below:

For the constriants $x + y \le 60$, $5x + y \le 100$ and $x \ge 0, y \ge 0$, the feasible region is:

Two linear programming problems (LPPs) have same bounded feasible region with three corner points $(0, 3), (4, 4), (7, 0)$. If $Z_1 = x - 3y$ and $Z_2 = 2x + y$ are objective functions of LPPs, then which of the following is/are correct?

A. only $Z_1$ maximizes at $(7, 0)$.

B. both $Z_1, Z_2$ minimize at $(0, 3)$.

C. both $Z_1, Z_2$ maximize at $(7, 0)$.

D. $Z_2$ maximizes at $(4, 4)$.

Choose the correct answer from the options given below:

In a LPP, Let R be the feasible region, then which of the following are TRUE?

A. If R is bounded, then the objective function Z has both a maximum and minimum value on R.

B. If R is unbounded, then the objective function Z may or may not have a maximum or minimum value.

C. If a optimal solution exists. It must occur at atleast one corner point of R.

D. If R is bounded, then maximum value will exist but minimum may or may not exist for an objective function Z.

Choose the correct answer from the options given below:

Ravi rides his motor cycle at 25 km per hour, he has to spend ₹ 4 per kilometer on petrol, if he rides at a faster speed of 40 km per hour, the petrol cost increases to ₹ 10 per kilometer. He can spend ₹ 200 on petrol and wishes to maximize distance he can travel within one hour. Which of the following is/are TRUE?

A. Maximum distance covered in one hour is 30 km

B. The distance covered at speed of 25km/hr is 50/3 km

C. The distance covered at speed of 25km/hr is $\frac{25}{2}$ km

D. The distance covered at speed of 40km/hr is $\frac{75}{4}$ km

Choose the correct answer from the options given below:

The maximum value of $z = 4x + 2y$, subjected to the constraints:

$2x + 3y \le 18$, $x + y \ge 5$;

$x, y \ge 0$, is

The corner points O, A, B, C, D and E of the bounded feasible region determined by the system of linear constraints are shown in the given figure.

If $z = 3x - 4y$ be the objective function, then the minimum of z, is:

If $z = px + qy$, where $p, q > 0$, is the objective function. Then the condition on p and q so that the maximum value of z occurs at A(4, 10) and B(6, 8), is: