Algebra

Linear Programming

Medium

core

For an LPP: Maximize $z = 3x + 9y$ , $x \geq 0, y \geq 0$ , the feasible region OAB is shown in the figure, then the other constraints are

$x + 3y \leq 60, x \geq y$

$x + 3y \geq 60, x \leq y$

$x + 3y \geq 60, x \geq y$

$x + 3y \leq 60, x \leq y$

✅ Correct Option: 4

The Linear Programming Problem requires identifying the missing constraints from the feasible region OAB shown in the graph.

Given information:

Objective function: Maximize $z = 3x + 9y$

Basic constraints: $x \geq 0, y \geq 0$ (first quadrant)

Feasible region: Triangle OAB

From the graph, identify the three vertices of triangle OAB:

$O = (0, 0)$ (Origin)

$A = (0, 20)$ (on the y-axis)

$B = (20, 20)$ (in the first quadrant)

These vertices help us determine the boundary lines.

The feasible region is bounded by three lines. Two are already given: $x = 0$ (y-axis) and $y = 0$ (x-axis).

The third boundary is the slanted line passing through A and another point on the x-axis.

From the options, try $x + 3y = 60$ :

When $x = 0$ :

$3y = 60$

$y = 20$ ✓ (matches point A)

When $y = 0$ :

$x = 60$ (gives point $(60, 0)$ on x-axis)

Since the feasible region OAB is below this line (towards the origin):

$x + 3y \leq 60$

The line through $O(0,0)$ and $B(20,20)$ is found by noting both coordinates are equal.

This line is $x = y$ .

The feasible region OAB lies above or on this line (closer to the y-axis).

Therefore:

$x \leq y$

The complete set of constraints is:

$x \geq 0, y \geq 0$

$x + 3y \leq 60$

$x \leq y$

The other constraints are $x + 3y \leq 60$ and $x \leq y$ .

Therefore, the answer is Option 4.

2023: 23 May Shift 3

A manufacturing company makes two models M $_1$ and M $_2$ of a product. Each piece of M $_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of M $_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs.800 on each piece of M $_1$ and Rs.1200 on each piece of M $_2$

The above Linear Programming Problem [LPP] is given by

2025: 27 May Shift 1

The corner points of the bounded feasible region determined by a set of constraints in an LPP are $P(0, 5)$ , $Q(3, 5)$ , $R(5, 0)$ and $S(4, 1)$ . If the objective function is $z = ax + 2by$ , where, $a, b > 0$ , then the condition on $a$ and $b$ such that the maximum value of $z$ occurs at $Q$ and $S$ is

2026: 30 May Shift 1

In reference to a linear programming problem (LPP), which of the following statements are true?

A. The optimal value of the objective function is attained at the points given by intersections of inequation with the axes only.

B. The objective function of a LPP is a linear function to be optimized.

C. Every LPP admits an optimal solution.

D. The region represented by the inequation system, $x, y\geq0$ , $x+2y\leq4, 3x+y\geq3, 4x+3y\geq6$ is bounded in the first quadrant.

Choose the correct answer from the options given below:

2025: 21 May Shift 2

About linear programming problem (LPP), which of the following statements are correct?

(A) In a LPP, the linear inequalities or restrictions on the variables are called linear constraints.

(B) If the feasible region for an LPP is unbounded, then the maximum or minimum value of the objective function $Z = ax + by$ never exists.

(D) The common region determined by all the linear constraints of an LPP is called the feasible region.

Choose the correct answer from the options given below:

2026: 30 May Shift 2

If the objective function for a LPP is $Z=3x+5y$ and the corner points of the bounded feasible region are (0, 0), (6, 0), (3, 5) and (0, 3), then the value of $|max(Z) - min(Z)|$ is:

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:

For an LPP: Maximize z=3x+9yz = 3x + 9yz=3x+9y, x≥0,y≥0x \geq 0, y \geq 0x≥0,y≥0, the feasible region OAB is shown in the figure, then the other constraints are

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

For an LPP: Maximize $z = 3x + 9y$ , $x \geq 0, y \geq 0$ , the feasible region OAB is shown in the figure, then the other constraints are