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

The feasible region for a LPP is shown in the figure. Let \[Z=3x-4y\] be the objective function Minimum of Z occur at

A) (0, 0)

B) (0, 8)

C) (5, 0)

D) (4, 10).

Correct Answer: B

Solution :

Construct the following table of values of the objective functions: Corner Points Value of Z = 3x - 4y

Corner Points	Value of \[Z=3x-4y\]
(0, 0) (5, 0) (6, 5) (6, 8) (4, 10) (0, 8)	\[3\times 0-4\times 0=0\] \[3\times 5-4\times 0=15\] \[3\times 6-4\times 5=-2\] \[3\times 6-4\times 8=-14\] \[3\times 4-4\times 10=-28\] \[3\times 0-4\times 8=-32\to Minimum\]

Minimum of Z = - 32 at (0, 8)