question_answer

The maximum value \[z=5x+2y,\]subject to the constraints \[x+y\le 7,x+2y\le 10,x,y\ge 0\]is

A) 10

B) 26

C) 35

D) 70

Correct Answer: C

Solution :

[c] Change the inequalities into equations and draw the graph of lines, thus we get the required feasible region as shown below. The region bounded by the vertices A (0, 5), B (4, 3), C (7, 0). The objective function is maximum at C (7, 0) and Max \[z=5\times 7+2\times 0=35.\]