Question

Given the linear program

Max 3x+4y

s.t. -x+2y≤8

x+2y≤12

2x+y≤16

x,y≥0

a. Write the problem in standard form. Identify slack/surplus variables.

b. List all the extreme points. You must write down the values for x and y for each extreme point.

c. Find the optimal solution by comparing the extreme points.

d. What are the values of the three slack/surplus variables at the optimal solution?

Answer 1

(B)

The co-ordinates of O is (0,0) the value of Z is 0

A is (0,4) the value of Z is 16

B is (2,5) the value of Z is 26

F is (6.6666,2.6666) the value of Z is 30.6667

H is (8,0) the value of Z is 24.

(C) The optimal value is given at F and its value is 30.667

(D) S₁ = 8 + 6.66666 - 2(2.6666) = 9.3346

S₂ = 12 - 6.6666 - 2 (2.666) = 0

S₃ = 16 - ( 2 x 6.6666) - 2.6666 = 0

Value of Slack 1 is 9.3346 while value of Slack 2 and 3 at optimal solution is 0