Question

Solve the following linear programming problem. Maximize: z = 21x + 11y subject to: 5x + 3y = 15 7x + y = 15 x20, y20

Answer 1

Maximize z=21x+11y

Subject to: 5x+3y≤15 (Red line)

7x+y≤15 (Blue line)

x≥0, y≥0

у 5 4 3- 2- (1.875, 1.875) -1- 0 1 2 3 4 Х

The corner points are :

(1.875,1.875)=21*1.875+11*1.875= 60

(3,0)= 21*3+11*0= 63

(0,5)= 21*0+11*5=55

so

Maximum value= 63

maximum occurs at a point (3,0)