Engineering Optimization: Theory and Practice, Fourth Edition

240 Linear Programming II: Additional Topics and Extensions

4.2 Maximizef=^15 x 1 +^6 x 2 +^9 x 3 +^2 x 4

subject to

10 x 1 + 5 x 2 + 25 x 3 + 3 x 4 ≤ 50

12 x 1 + 4 x 2 + 12 x 3 +x 4 ≤ 48

7 x 1 +x 4 ≤ 35

xi≥ 0 , i=1 to 4

4.3 Minimizef=^2 x 1 +^3 x 2 +^2 x 3 −x 4 +x 5

subject to

3 x 1 − 3 x 2 + 4 x 3 + 2 x 4 −x 5 = 0

x 1 +x 2 +x 3 + 3 x 4 +x 5 = 2

xi≥ 0 , i= 1 , 2 ,... , 5

4.4 Discuss the relationships between the regular simplex method and the revised simplex

method.

4.5 Solve the following LP problem graphically and by the revised simplex method:

Maximizef=x 2

subject to

−x 1 +x 2 ≤ 0

− 2 x 1 − 3 x 2 ≤ 6

x 1 , x 2 unrestricted in sign

4.6 Consider the following LP problem:

Minimizef= 3 x 1 +x 3 + 2 x 5

subject to

x 1 +x 3 −x 4 +x 5 = − 1

x 2 − 2 x 3 + 3 x 4 + 2 x 5 = − 2

xi≥ 0 , i=1 to 5

Solve this problem using the dual simplex method.

4.7 Maximizef=^4 x 1 +^2 x 2

subject to

x 1 − 2 x 2 ≥ 2

x 1 + 2 x 2 = 8