For the linear programming problem (LPP), the objective function … - Vidyadip

MCQ

For the linear programming problem $\text{(LPP),}$ the objective function is $Z= 4x+3y$ and the feasible region determined by a set of constraints is shown in the graph:

Which of the following statements is true?

A
Maximum value of $Z$ is at $R(40, 0)$
✓
Maximum value of $Z$ is at $Q(30, 20)$
C
Value of $Z$ at $R(40, 0)$ is less than the value at $P(0,40)$
D
The value of $Z$ at $Q(30, 20)$ is less than the value at $R(40, 0)$

✓

Answer

Correct option: B.

Maximum value of $Z$ is at $Q(30, 20)$

Corner point	Value of the objective function $Z = 4x + 3y$
$1. O(0, 0)$	$z = 0$
$2. R(40, 0)$	$z = 160$
$3. Q(30,20)$	$z = 120 + 60 = 180$
$4. P(0,40)$	$z = 120$

Since, the feasible region is bounded so the maximum value of the objective function $z = 180$ is at $Q(30, 20)$

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