Engineering Optimization: Theory and Practice, Fourth Edition

166 Linear Programming I: Simplex Method

9 x+ 7 y≤ 108

3 x+ 7 y≤ 70

2 x− 5 y≥ − 35

x≥ 0 , y≥ 0

3.28 Minimizef=x− 4 y

subject to

x−y≥ − 4

4 x+ 5 y≤ 45

5 x− 2 y≤ 20

5 x+ 2 y≤ 10

x≥ 0 , y≥ 0

3.29 Maximizef=x− 4 y

subject to

x−y≥ − 4

4 x+ 5 y≤ 45

5 x− 2 y≤ 20

5 x+ 2 y≥ 10

x≥ 0 , yis unrestricted in sign

3.30 Minimizef=x− 4 y

subject to

x−y≥ − 4

4 x+ 5 y≤ 45

5 x− 2 y≤ 20

5 x+ 2 y≥ 10

x≥ 0 , y≥ 0

3.31 Rework Problem 3.30 by changing the objective to Maximizef=x− 4 y.

3.32 Minimizef= 4 x+ 5 y