Algebra

Linear Programming

Easy

core

The corner points of a bounded feasible region determined by the following system of linear inequalities $x + 3y \leq 60, x + y \geq 10$ , $x \leq y$ , $x \geq 0$ , $y \geq 0$ are (0,10), (5,5), (15, 15) and (0, 20). Let $z = 2px + qy$ , $p, q > 0$ . If maximum of z occurs at both (15, 15) and (0, 20), then the relation between p and q is

$3p = 2q + 1$

$3p = 4q$

$6p = q$

$2p = 3q$

✅ Correct Option: 3

The maximum value of $z$ occurs at two corner points: $(15, 15)$ and $(0, 20)$ .

In linear programming, when the maximum occurs at two corner points, both points give the same maximum value of $z$ and the objective function line is parallel to the edge joining these two points.

At point $(15, 15)$ :

$z = 2p(15) + q(15)$

$z = 30p + 15q$

At point $(0, 20)$ :

$z = 2p(0) + q(20)$

$z = 20q$

Since both points give the maximum value:

$30p + 15q = 20q$

$30p = 20q - 15q$

$30p = 5q$

$6p = q$

Therefore, the relation between $p$ and $q$ is $q = 6p$ .

2022: 6 Aug Shift 2

The optimal solution of the Linear Programming problem

Maximize $Z = 3x_1 + 5x_2$ ,

s.t. $3x_1 + 2x_2 \leq 18$

$x_1 \leq 4$

$x_2 \leq 6$

$x_1 \geq 0, x_2 \geq 0$ is

2022: 16 July Shift 2

The type of feasible region and its corner points are.

A. bounded

B. unbounded

C. (0,5), (2,4), (10,0)

D. (0,8), (2,4), (4,0)

E. (0,8), (2,4), (10,0)

Choose the correct answer from the options given below:

2025: 14 May Shift 1

Which of the following is NOT a basic requirement of the linear programming problem (LPP)?

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

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: 26 May Shift 2

If the objective function z = 4x + 3y has maximum value on a line joining points (3, a) and (b, 2) where a > 0, b > 0 such that a - b = 2, then the maximum value of z is:

Solution

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