Algebra

Linear Programming

Medium

common

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0,0)$ , $(4,0)$ , $(2,4)$ and $(0,5)$ . If maximum value of $z = ax + by$ , where $a,b > 0$ , occurs at both $(2,4)$ and $(4,0)$ then

$a = 2b$

$2a = b$

$a = b$

$3a = b$

✅ Correct Option: 1

The corner points of the bounded feasible region are $(0,0)$ , $(4,0)$ , $(2,4)$ and $(0,5)$ .

The maximum value of $z = ax + by$ , where $a,b > 0$ , occurs at both $(2,4)$ and $(4,0)$ .

In linear programming, when the maximum occurs at two corner points, those points must give the same value of $z$ .

At point $(2,4)$ :

$z = a(2) + b(4)$

$z = 2a + 4b$

At point $(4,0)$ :

$z = a(4) + b(0)$

$z = 4a$

Since both points give the maximum value:

$2a + 4b = 4a$

$4b = 4a - 2a$

$4b = 2a$

$2b = a$

Therefore, $a = 2b$ .

2025: 30 May Shift 2

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

2026: 19 May Shift 1

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

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

$x, y \ge 0$ , is

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Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

2025: 14 May Shift 1

Which of the following statements are correct in reference to the linear programming problem(LPP):

Maximize ${Z} = 5x + 2y$

subject to the following constraints

$3x + 5y \leq 15$ , $5x + 2y \leq 10$ , $x \geq 0, y \geq 0$ .

(A) The LPP has a unique optimal solution at $(2, 0)$ only.

(B) The feasible region is bounded with corner points $(0, 0)$ , $(2, 0)$ , $(20/19, 45/19)$ and $(0, 3)$ .

(D) The feasible region is unbounded.

Choose the correct answer from the options given below:

2025: 3 June Shift 2

If $z = 3x + 4y$ be the objective function of a of a linear programming problem (LPP) and (3, 1), (2, 4), (0, 4), (5, 0) be corner points of the bounded feasible region. Then the maximum value of objective function is

2026: 19 May Shift 2

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:

The corner points of the bounded feasible region determined by the system of linear inequalities are (0,0)(0,0)(0,0), (4,0)(4,0)(4,0), (2,4)(2,4)(2,4) and (0,5)(0,5)(0,5). If maximum value of z=ax+byz = ax + byz=ax+by, where a,b>0a,b > 0a,b>0, occurs at both (2,4)(2,4)(2,4) and (4,0)(4,0)(4,0) then

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CUET Mathematics Past Year Questions (Topic-Wise)

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0,0)$ , $(4,0)$ , $(2,4)$ and $(0,5)$ . If maximum value of $z = ax + by$ , where $a,b > 0$ , occurs at both $(2,4)$ and $(4,0)$ then