Algebra

Linear Programming

Medium

core

The corner points of the bounded feasible region for an LPP 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

120

180

✅ Correct Option: 3

The corner points of the bounded feasible region are: $(5, 5)$ , $(15, 15)$ , $(0, 20)$ , and $(0, 10)$ .

The objective function is $z = 3x + 9y$ .

In Linear Programming, the maximum and minimum values of the objective function occur at the corner points of the feasible region.

At point $(5, 5)$ :

$z = 3(5) + 9(5)$

$z = 15 + 45$

$z = 60$

At point $(15, 15)$ :

$z = 3(15) + 9(15)$

$z = 45 + 135$

$z = 180$

At point $(0, 20)$ :

$z = 3(0) + 9(20)$

$z = 0 + 180$

$z = 180$

At point $(0, 10)$ :

$z = 3(0) + 9(10)$

$z = 0 + 90$

$z = 90$

The values of $z$ are: $60, 180, 180, 90$

Maximum value of $z = 180$

Minimum value of $z = 60$

$\text{maximum}(z) - \text{minimum}(z) = 180 - 60$

$= 120$

Therefore, the value of $\text{maximum}(z) - \text{minimum}(z) = 120$

2025: 13 May Shift 2

The feasible region of the linear programming problem is represented below:

The constraints of this LPP are

2025: 2 June Shift 1

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

2025: 2 June Shift 1

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?

2026: 18 May Shift 1

If the corner points of the bounded feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5), then the minimum value of the objective function $z = 2x+3y$ occurs at

2022: 25 May Shift 1

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 :

2026: 21 May Shift 1

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)

(D) (90, 10)

Choose the correct answer from the options given below:

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

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CUET Mathematics Past Year Questions (Topic-Wise)

The corner points of the bounded feasible region for an LPP 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