12th Class Mathematics Linear Programming Question Bank Case Based (MCQs) - Linear Programming

Directions: (11 - 15)

Corner points of the feasible region for an LPP are (0, 3), (5, 0), (6, 8), (0, 8). Let \[Z\text{ }=4x-6y\] be the objective function.

Based on the above information, answer the following questions:

The minimum value of Z occurs at

A) (6, 8)

B) (5, 0)

C) (0,3)

D) (0,8)

Correct Answer: D

Solution :

Construct the following table of values of objective function

Corner Points	Value of \[Z=6x+3y\]
(0, 3) (5, 0) (6, 8) (0, 8)	\[4\times 0-6\times 3=-18\] \[4\times 5-6\times 0=20\] \[4\times 6-6\times 8=-24\] \[4\times 0-6\times 8=-48\]

Minimum value of Z is -48 which occurs at (0.8).