Test1 ECG 795 Optimization, Fall2009
Problem 1 (10 Points) Solve the following optimization problem by hand. Moreover, give a graphical
solution also.
Minimize : z= 0.04(x1−95)2+ 0.02(x2−125)2
subject to : 0.2x1+ 0.2x2≤20
0.8x1+ 0.3x2≤60
with : x1≥0, x2≥0
Problem 2 (10 Points) Put the following program in standard form and provide an initial basic feasible
solution.
Minimize : z= 25x1+ 30x2
subject to : 4x1+ 7x2≥1
8x1+ 5x2≥3
6x1+ 9x2≥ −2
with : x1≥0, x2≥0
Problem 3 (10 Points) Prove that the objective function of the following system assumes its minimum
at an extreme point of ℑ, provided a minimum exists and that ℑis bounded.
Minimize : z=CTX
subject to : AX =B
with : X≥0
Dr. Pushkin Kachroo: pushkin@unlv.edu http://faculty.unlv.edu/pushkin