Question

Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).

Let F = 4x + 6y be the objective function. The Minimum value of F occurs at

A. (0, 2) only
B. (3, 0) only
C. the midpoint of the line segment joining the points (0, 2) and (3, 0) only
D. any point on the line segment joining the points (0, 2) and (3, 0).

Answer 1

F = 4x + 6y

Corner points - (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).

Value of F at corner points –

At (0, 2), F = 12

At (3, 0), F = 12

At (6, 0), F = 24

At (6, 8), F = 72

At (0, 5), F = 30

Feasible region –

As, feasible region to be bounded so it is a closed polygon.

So, minimum value of F = 12 are at (3, 0) and (0, 2).

Therefore, minimum value of F occurs at, any point on the line segment joining the points (0, 2) and (3, 0).