Algebra

Linear Programming

Medium

core

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

$a - 5b = 0$

$a - 3b = 0$

$a - 2b = 0$

$a - 8b = 0$

✅ Correct Option: 4

The Linear Programming Problem has corner points P(0, 5), Q(3, 5), R(5, 0), and S(4, 1) with objective function $z = ax + 2by$ where $a, b > 0$ .

When the maximum occurs at two corner points, both points must give the same z-value, and this value must be greater than or equal to the z-values at other corner points.

At P(0, 5):

$z = a(0) + 2b(5)$

$z = 10b$

At Q(3, 5):

$z = a(3) + 2b(5)$

$z = 3a + 10b$

At R(5, 0):

$z = a(5) + 2b(0)$

$z = 5a$

At S(4, 1):

$z = a(4) + 2b(1)$

$z = 4a + 2b$

Since maximum occurs at both Q and S, their z-values must be equal:

$3a + 10b = 4a + 2b$

$10b - 2b = 4a - 3a$

$8b = a$

$a - 8b = 0$

Therefore, the condition is $a - 8b = 0$ .

2025: 19 May Shift 1

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

2026: 25 May Shift 1

A company makes two types of cakes: type A and type B. it costs ₹ 360 to make a type A cake and ₹ 120 to make a type B cake. The company can make atmost 300 cakes and spend atmost ₹ 72,000 a day, the number of cakes of type B ( $y$ ) cannot exceed the number of type A ( $x$ ) cakes by more than 200.

The company makes a profit of ₹ 200 on each type A cake and ₹ 50 on each type B cake. A LPP to maximize the profit (₹) is

2025: 3 June Shift 1

The objective function of an LPP is $z = ax + \beta y, (a, \beta > 0)$ in that has to be maximized/minimized subject to constraints

$x + y \leq 2$ , $x \geq 0$ , $y \geq 0$ . Then max (z) $-$ min (z) is equal to

2025: 30 May Shift 1

Which one of the following set of constraints represents the shaded region given below?

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: 2 June Shift 1

Linear inequalities corresponding to the shaded feasible region OABCO in the given figure are

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)