Algebra

Linear Programming

Medium

core

Which one of the region I, II, III, IV is represented by the constraints

$x + 3y \le 60, x + y \ge 10, x \le y, x \ge 0, y \ge 0$

Region I , Quadrilateral ABEF

Region II, $\triangle$ OAB

Region III, $\triangle$ OCB

Region IV, Quadrilateral BCDE

✅ Correct Option: 1

The boundary lines meet at $(0,10)$ , $(5,5)$ , $(15,15)$ and $(0,20)$ , so the feasible set is a quadrilateral, not a triangle.

This eliminates the two triangular options, and the region lying above $x+y=10$ , below $x+3y=60$ and left of $x=y$ is the quadrilateral marked as Region I.

Note: The labelled figure is not reproduced in this transcription; the region was identified from the four vertices computed above.

2026: 18 May Shift 1

If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and $z = px + qy$ , $(p,q > 0)$ is an objective function. Then the relation between $p$ and $q$ , when $z$ is maximum at $D(4,10)$ and $C(6,8)$ , is:

2026: 25 May Shift 1

Which of the following group of constraints represents the feasible region given as shaded area below ?

2025: 15 May Shift 2

If the objective function for a linear programming problem (LPP) is $Z = 4x + 5y$ and the corner points of the bounded feasible region are (9, 0), (4, 3), (2, 5), and (0,8), then the minimum value of Z is:

2026: 21 May Shift 2

Consider a LPP with objective function $Z = px + qy$ subjected to certain constraints with a bounded feasible region such that maximum $Z = 80$ and minimum $Z = 52$ , which occur at the corner points $(0, 8)$ and $(2, 4)$ respectively, Then the value of $p+q$ is:

2026: 18 May Shift 2

The feasible region of an LPP is a bounded region by vertices (4, 18), (6, 12), (40, 0) and (15, 0). Then the point (15, 15) lies in the

A. open half plane of $x+2y<40$ .

B. closed half plane of $3x+y\ge 30$ .

C. closed half plane of $4x+3y\ge 60$ .

D. feasible region of the given LPP.

Choose the correct answer from the options given below:

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

Which one of the region I, II, III, IV is represented by the constraints x+3y≤60,x+y≥10,x≤y,x≥0,y≥0x + 3y \le 60, x + y \ge 10, x \le y, x \ge 0, y \ge 0x+3y≤60,x+y≥10,x≤y,x≥0,y≥0

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Which one of the region I, II, III, IV is represented by the constraints

$x + 3y \le 60, x + y \ge 10, x \le y, x \ge 0, y \ge 0$