Question

Assertion (A) The maximum value of
$Z=11x+7y$
subject to the constraints
$2x+y\le 6$
$x\le 2$
$x\ge 0,y\ge 0$
occurs at the corner point $(0,6)$.
Reason (R) If the feasible region of the given LPP is bounded, then the maximum and minimum value of the objective function occurs at corner points.

• A. Both A and R are correct; R is the correct explanation of A
• B. Both A and R are correct; R is not the correct explanation
• C. A is correct; R is incorrect
• D. R is correct; A is incorrect

Answer 1

Answer: (A)

The given LPP is
Maximise $Z=11x+7y$
Subject to the constraints are
$2x+y\le 6$
$x\le 2$
$x\ge 0,y\ge 0$
The corresponding graph of the above LPP is

from the above graph, we see that the shaded region is the feasible region $OABC$ which is bounded.
$\therefore$ The maximum value of the objective function $Z$ occurs at the corner points.
The corner points are $O(0,0),A(0,6),B(2,2),C(2,0)$.
The values of $Z$ at these corner points are given by

Corner point	Corresponding value of $z-11x+7y$
$(0,0)$	0
$(0,6)$	$42\leftarrow$ Maximum
$(2,2)$	36
$(2,0)$	22

Thus, the maximum valuo of $Z$ is 42 which occurs at the point $(0,6)$.