Algebra

Linear Programming

Medium

core

Consider the LPP: Max $Z = 5x + 3y$ subject to $3x + 5y \leq 15, 5x + 2y \leq 10, x \geq 0, y \geq 0$

Match List-I with List-II

List-I List-II
(A) Objective function (I) $3x + 5y \geq 15$
(B) One constraint (II) $x, y \geq 0$
(C) Non-negative restrictions (III) $Z = 5x + 3y$
(D) Point $(1, 2)$ does not lie in the region (IV) $3x + 5y \leq 15$

Choose the correct answer from the options given below:

List-I	List-II
(A) Objective function	(I) $3x + 5y \geq 15$
(B) One constraint	(II) $x, y \geq 0$
(C) Non-negative restrictions	(III) $Z = 5x + 3y$
(D) Point $(1, 2)$ does not lie in the region	(IV) $3x + 5y \leq 15$

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (III), (B) - (I), (C) - (II), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

✅ Correct Option: 2

The given LPP is:

Maximize $Z = 5x + 3y$

Subject to:

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

The objective function is what we want to maximize or minimize in an LPP.

Here, we want to maximize $Z = 5x + 3y$

(A) matches with (III): $Z = 5x + 3y$

Constraints are the conditions/restrictions given in the problem.

The constraints are:

$3x + 5y \leq 15$
$5x + 2y \leq 10$

Option (IV) gives: $3x + 5y \leq 15$ (which is one of the constraints)

(B) matches with (IV): $3x + 5y \leq 15$

Non-negative restrictions ensure that variables cannot be negative.

Here: $x \geq 0, y \geq 0$ (which is the same as $x, y \geq 0$ )

Testing point $(1, 2)$ in option (I): $3x + 5y \geq 15$

$3(1) + 5(2) = 3 + 10 = 13$

Since $13 < 15$ , point $(1, 2)$ does not satisfy the constraint $3x + 5y \geq 15$

Therefore, it does not lie in that region.

(D) matches with (I): $3x + 5y \geq 15$

List-I	Matches	List-II
(A) Objective function	→	(III) $Z = 5x + 3y$
(B) One constraint	→	(IV) $3x + 5y \leq 15$
(C) Non-negative restrictions	→	(II) $x, y \geq 0$
(D) Point $(1, 2)$ does not lie in the region	→	(I) $3x + 5y \geq 15$

2022: 10 Aug Shift 1

A manufacturer of electronic circuit has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs. 50 and that on type B circuit is Rs. 60, identify the constraints for this LPP, if it was assumed that x circuit B of type A and y circuits of type B was produced by the manufacturer.

A. $x + 2y \geq 15$

B. $2x + y \leq 20$

C. $x + 2y \leq 12$

D. $x, y \leq 0$

Choose the correct answer from the options given below

2026: 19 May Shift 2

Ravi rides his motor cycle at 25 km per hour, he has to spend ₹ 4 per kilometer on petrol, if he rides at a faster speed of 40 km per hour, the petrol cost increases to ₹ 10 per kilometer. He can spend ₹ 200 on petrol and wishes to maximize distance he can travel within one hour. Which of the following is/are TRUE?

A. Maximum distance covered in one hour is 30 km

B. The distance covered at speed of 25km/hr is 50/3 km

C. The distance covered at speed of 25km/hr is $\frac{25}{2}$ km

D. The distance covered at speed of 40km/hr is $\frac{75}{4}$ km

Choose the correct answer from the options given below:

2023: 22 May Shift 3

The feasible region for an LPP is shown below. Let $Z = 3x - 4y$ be the objective function. Maximum of Z occurs at :

2026: 29 May Shift 2

The number of feasible solutions of the linear programming problem as

Maximum $z=15x+30y$ subject to the constraints

$3x+y \leq 12$

$x+2y \leq 10$

$x \geq 0, y \geq 0$

2025: 3 June Shift 2

The region represented by the system of inequalities $x, y \geq 0, y \leq 6, x + y \leq 3$

2026: 21 May Shift 2

Consider a LPP with objective function $z = ax + by$ . If its feasible region R is bounded, then $z$

Solution

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