Algebra

Linear Programming

Medium

core

For the LPP: minimize $z = 6x + 3y$ subject to the constraints

$4x + y \geq 80$

$x + 5y \geq 115$

$3x + 2y \leq 150$

$x \geq 0, y \geq 0$ then the minimum value of z is

150

228

120

100

✅ Correct Option: 1

For the LPP: minimize $z = 6x + 3y$ subject to the constraints:

$4x + y \geq 80$

$x + 5y \geq 115$

$3x + 2y \leq 150$

$x \geq 0, y \geq 0$

The minimum value occurs at a corner point of the feasible region.

Finding the intersection of $4x + y = 80$ and $x + 5y = 115$ :

$y = 80 - 4x$

$x + 5(80 - 4x) = 115$

$x + 400 - 20x = 115$

$-19x = -285$

$x = 15$

$y = 80 - 4(15)$

$y = 20$

Corner point: $(15, 20)$

Finding the intersection of $4x + y = 80$ and $3x + 2y = 150$ :

$y = 80 - 4x$

$3x + 2(80 - 4x) = 150$

$3x + 160 - 8x = 150$

$-5x = -10$

$x = 2$

$y = 80 - 4(2)$

$y = 72$

Corner point: $(2, 72)$

Finding the intersection of $x + 5y = 115$ and $3x + 2y = 150$ :

$x = 115 - 5y$

$3(115 - 5y) + 2y = 150$

$345 - 15y + 2y = 150$

$-13y = -195$

$y = 15$

$x = 115 - 5(15)$

$x = 40$

Corner point: $(40, 15)$

Evaluating $z = 6x + 3y$ at each corner point:

At $(15, 20)$ :

$z = 6(15) + 3(20)$

$z = 90 + 60$

$z = 150$

At $(2, 72)$ :

$z = 6(2) + 3(72)$

$z = 12 + 216$

$z = 228$

At $(40, 15)$ :

$z = 6(40) + 3(15)$

$z = 240 + 45$

$z = 285$

The minimum value of $z$ is $150$ at point $(15, 20)$ .

2025: 14 May Shift 1

The corner points of the feasible region of the LPP: Minimize $Z = -50x + 20y$ subject to $2x - y \geq -5$ , $3x + y \geq 3$ , $2x - 3y \leq 12$ and $x, y \geq 0$ are

2025: 15 May Shift 1

The maximum value of the objective function $z = 2x + 3y$ of an L.P.P. subjected to the constraints $x - y \le 1$ , $x + y \le 3$ , $x, y \ge 0$ is

2022: 7 Aug Shift 2

The corner points of the feasible region determined by inequalities of LPP are $(4, 10)$ , $(6, 8)$ and $(6, 5)$ . Let $z = 3x + 4y$ be the objective function. Then the sum of maximum value of z and minimum value of z is :

2025: 22 May Shift 2

Consider the LPP: Maximize $z = 5x + 3y$ subject to $3x + 5y \leq 15$ , $5x + 2y \leq 10$ , $x,y \geq 0$ . The optimal feasible solution occurs at

2026: 22 May Shift 1

For a LPP, maximize $z=2x+3y$ , subjected to constraints:

$x\ge2, x\le7, y\le x, x+y\le10, x\ge0, y\ge0$

Which of the following statements are TRUE ?

(A) Vertices of feasible region are (2, 0), (7, 0), (7, 3), (5, 5) and (2, 2).

(B) Maximum $z=25$ at point (5, 5).

(D) The feasible region is unbounded.

Choose the correct answer from the options given below:

2025: 3 June Shift 1

A Linear Programming Problem (LPP) consists of which of the following components?

(A) Decision variables

(B) The graphical compliment

(D) The linear constraints

Choose the correct answer from the options given below:

For the LPP: minimize z=6x+3yz = 6x + 3yz=6x+3y subject to the constraints 4x+y≥804x + y \geq 804x+y≥80 x+5y≥115x + 5y \geq 115x+5y≥115 3x+2y≤1503x + 2y \leq 1503x+2y≤150 x≥0,y≥0x \geq 0, y \geq 0x≥0,y≥0 then the minimum value of z is

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CUET Mathematics Past Year Questions (Topic-Wise)

For the LPP: minimize $z = 6x + 3y$ subject to the constraints

$4x + y \geq 80$

$x + 5y \geq 115$

$3x + 2y \leq 150$

$x \geq 0, y \geq 0$ then the minimum value of z is