Question

By graphing the system of constraints, find the values of x and y that maximize the objective function. 25<=x<=75 y<=110 8x+6y=>720 y=>0 minimum for c=8x+5y a. c=100 b. c=225 2/3 c. c=633 1/3 d. c=86 2/3

Answer 1

Sketch the graph

x = 25
x = 75
y = 110
6y = 720 - 8x

and C = 8x + 5y

The minimum point for C is the point of intersection between 8x + 6y = 720 and x = 25

Substitute x = 25 into 8x + 6y = 720 we have:
8(25) + 6y = 720
200 + 6y = 720
6y = 720-200
6y = 520
y = ²⁶⁰/₃

Substitute x = 25 and y = ²⁶⁰/₃ into C
C = 8(25) + 5(²⁶⁰/₃) = 633¹/₃

Answer: Option C