Engineering Optimization: Theory and Practice, Fourth Edition

Problems 163

3.10 Find the solution of the following problem by the graphical method:

Minimizef=x 12 x 22

subject to

x 13 x 22 ≥e^3

x 1 x 24 ≥e^4

x 12 x 23 ≤e

x 1 ≥ 0 , x 2 ≥ 0

whereeis the base of natural logarithms.

3.11 Prove Theorem 3.6.

For Problems 3.12 to 3.42, use a graphical procedure to identify (a) the feasible region,

(b) the region where the slack (or surplus) variables are zero, and (c) the optimum

solution.

3.12 Maximizef=^6 x+^7 y

subject to

7 x+ 6 y≤ 42

5 x+ 9 y≤ 45

x−y≤ 4

x≥ 0 , y≥ 0

3.13 Rework Problem 3.12 whenxandyare unrestricted in sign.

3.14 Maximizef= 19 x+ 7 y

subject to

7 x+ 6 y≤ 42

5 x+ 9 y≤ 45

x−y≤ 4

x≥ 0 , y≥ 0

3.15 Rework Problem 3.14 whenxandyare unrestricted in sign.

3.16 Maximizef=x+ 2 y

subject to

x−y≥ − 8

5 x−y≥ 0

x+y≥ 8