Algebra

Linear Programming

Medium

applied

The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is

✅ Correct Option: 1

In Linear Programming Problems (LPP), the minimum or maximum value of the objective function occurs at one of the corner points of the feasible region.

From the graph, the corner points of the shaded feasible region are:

Point A: $(0, 3)$

Point B: $(3, 0)$

Point C: $(0, 6)$

Evaluating $Z = 11x + 7y$ at each corner point:

At point A: $(0, 3)$

$Z = 11(0) + 7(3)$

$Z = 0 + 21$

$Z = 21$

At point B: $(3, 0)$

$Z = 11(3) + 7(0)$

$Z = 33 + 0$

$Z = 33$

At point C: $(0, 6)$

$Z = 11(0) + 7(6)$

$Z = 0 + 42$

$Z = 42$

Comparing the values:

At point A: $Z = 21$
At point B: $Z = 33$
At point C: $Z = 42$

Therefore, the minimum value of $Z = 21$

2026: 31 May Shift 2

A LPP $max\,z = ax+by$ having bounded feasible region with vertices on $(2,1), (3,2), (5,6)$ and $(1,7)$ . Then which of following are TRUE?

A. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = 4a$

B. $max\,z$ occurs at $(1,7)$ and $(5,6)$ if $b = -4a$

C. $max\,z$ does not exist

D. if $max\,z$ occurs at $(1,7)$ and $(5,6)$ , then $max\,z$ occurs for infinite number of value of $x$ and $y$

Choose the correct answer from the options given below:

2025: 15 May Shift 1

If the optimal value of the objective function $z = px + y$ of an L.P.P occurs at two corner points (2, 11) and (4, 5) of its bounded feasible region, then its optimal value is

2025: 3 June Shift 2

Which of the following terms are associated with a linear programming problem?

(A) Constraints

(B) Independent events

(D) Objective function

Choose the correct answer from the options given below:

2026: 30 May Shift 1

For a LPP, the objective function is $z=4x+3y$ and the feasible region determined by a set of linear constraints is shown in the graph as a shaded portion. Which one of the following statement is true ?

2025: 29 May Shift 2

The feasible region of a linear programming problem is bounded. The corresponding objective function is Z= 3x-4y. The objective function attains

2022: 25 May Shift 1

The programming problem

Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)