The corner points of the feasible region for the Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8), (0, 5).

Question

The corner points of the feasible region for the Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let the objective function is Z= 4x +6y then the minimum value of the objective function occurs at

(a) (0, 2) only

(b) (3, 0) only

(c) The mid-point on the line segment joining the points (0,2) and (3,0)

(d) Any point on the line segment joining the points (0,2) and (3,0)

Answer 1

Correct option is (d) Any point on the line segment joining the points (0,2) and (3,0)

Corner Points   Value of Z

A (0, 2)      Z = 0 + 12 = 12

B (3, 0)      Z = 12 + 0 = 12

C (6, 0)     Z = 24 + 0 = 24

D (6,8)      Z = 24 + 48 = 72

E (0,5)      Z = 0 + 30 = 30

Minimum value of Z = 12