Maximize subject to the constraints

MATHEMATICS · Single correct · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

Maximize

Z = 7x + 5y

subject to the constraints

x + 2y \le 8,\; 3x + y \le 9,\; x \ge 0,\; y \ge 0

. The optimum value of

Z

and the point at which it occurs are (a)

Z = 27\, \text{at } (1,4)

(b)

Z = 31\, \text{at } (3,2)

(c)

Z = 29\, \text{at } (2,3)

(d)

Z = 28\, \text{at } (0,4)