Engineering Optimization: Theory and Practice, Fourth Edition

Problems 247

to ensure nonzero reserve strength in each failure mechanism. Also, suggest a suitable

technique for solving the problem. Assume that the moment capacities are restricted as

0 ≤Mi≤ 2 × 105 lb-in.,i= 1 , 2 ,... ,7. Data:x=100 in.,y=150 in.,P 1 =1000 lb,

andP 2 =500 lb.

4.43 Solve the LP problem stated in Problem 4.9 using MATLAB (interior method).

4.44 Solve the LP problem stated in Problem 4.12 using MATLAB (interior method).

4.45 Solve the LP problem stated in Problem 4.13 using MATLAB (interior method).

4.46 Solve the LP problem stated in Problem 4.36 using MATLAB (interior method).

4.47 Solve the LP problem stated in Problem 4.37 using MATLAB (interior method).

4.48 Solve the following quadratic programming problem using MATLAB:

Maximizef= 2 x 1 +x 2 −x 12

subject to 2x 1 + 3 x 2 ≤ 6 , 2 x 1 +x 2 ≤ 4 , x 1 ≥ 0 , x 2 ≥ 0

4.49 Solve the following quadratic programming problem using MATLAB:

Maximizef= 4 x 1 + 6 x 2 −x 12 −x 22

subject tox 1 +x 2 ≤ 2 , x 1 ≥ 0 , x 2 ≥ 0

4.50 Solve the following quadratic programming problem using MATLAB:

Minimizef=(x 1 − 1 )^2 +x 2 − 2

subject to −x 1 +x 2 − 1 = 0 , x 1 +x 2 − 2 ≤ 0 , x 1 ≥ 0 , x 2 ≥ 0

4.51 Solve the following quadratic programming problem using MATLAB:

Minimizef=x^21 +x 22 − 3 x 1 x 2 − 6 x 1 + 5 x 2

subject tox 1 +x 2 ≤ 4 , 3 x 1 + 6 x 2 ≤ 20 , x 1 ≥ 0 , x 2 ≥ 0