Algebra

Linear Programming

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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

✅ Correct Option: 3

The objective function is Maximize $z = 2x + 3y$ .

In linear programming, the maximum value occurs at one of the corner points of the feasible region.

The corner points are $(0, 0)$ , $(1, 2)$ , and $(1, 1)$ .

Evaluating $z = 2x + 3y$ at each corner point:

At point $(0, 0)$ :

$z = 2(0) + 3(0)$

$z = 0$

At point $(1, 2)$ :

$z = 2(1) + 3(2)$

$z = 2 + 6$

$z = 8$

At point $(1, 1)$ :

$z = 2(1) + 3(1)$

$z = 2 + 3$

$z = 5$

Comparing the values:

At $(0, 0)$ : $z = 0$
At $(1, 2)$ : $z = 8$
At $(1, 1)$ : $z = 5$

The maximum value is $8$ , occurring at corner point $(1, 2)$ .

Therefore, the optimal value is $8$ .

2024: 16 May Shift 1

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2026: 18 May Shift 2

If a, b, c > 0 and $ax+by>c$ , then its graph represents:

2023: 30 May Shift 3

The feasible region for a LPP is shown in the given figure. The maximum value of $z = 2x + 5y$ 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:

2025: 26 May Shift 2

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

2026: 12 May Shift 2

The feasible region for an LPP is shown in the given figure. Let $Z=3x+4y$ be the objective function. Then which of the following is/are TRUE?

(A) The minimum value of Z is 156

(B) The minimum value of Z is 152

(D) Neither minimum nor maximum value of Z exists

Choose the correct answer from the options given below:

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

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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