Algebra

Linear Programming

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

✅ Correct Option: 1

The maximum value of $z = 5x + 7y$ is found subject to the constraints $x + y \leq 5$ , $x \geq 0$ , $y \geq 0$ .

In linear programming, the maximum or minimum value occurs at a corner point (vertex) of the feasible region.

The corner points are where the boundary lines meet.

When $x = 0$ and $y = 0$ : $(0, 0)$

When $y = 0$ and $x + y = 5$ , then $x = 5$ : $(5, 0)$

When $x = 0$ and $x + y = 5$ , then $y = 5$ : $(0, 5)$

Evaluating $z = 5x + 7y$ at each corner point:

At $(0, 0)$ :

$z = 5(0) + 7(0)$

$z = 0$

At $(5, 0)$ :

$z = 5(5) + 7(0)$

$z = 25$

At $(0, 5)$ :

$z = 5(0) + 7(5)$

$z = 35$

Comparing the values: $0$ , $25$ , and $35$

The maximum value is $35$ , which occurs at the point $(0, 5)$ .

2025: 22 May Shift 2

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:

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

2025: 16 May Shift 1

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

2025: 14 May Shift 2

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

2026: 19 May Shift 2

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:

2026: 29 May Shift 2

The number of feasible solutions of the linear programming problem as

Maximum $z=15x+30y$ subject to the constraints

$3x+y \leq 12$

$x+2y \leq 10$

$x \geq 0, y \geq 0$

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

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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