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Solved Problem on Optimization - Test 1 - Fall 2009 | ECG 795, Exams of Electrical and Electronics Engineering

Material Type: Exam; Professor: Kachroo; Class: Advanced Special Topics in Electrical Engineering; Subject: Electrical And Computer Engineering; University: University of Nevada - Las Vegas; Term: Fall 2009;

Typology: Exams

2009/2010

Uploaded on 02/24/2010

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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(x195)2+ 0.02(x2125)2
subject to : 0.2x1+ 0.2x220
0.8x1+ 0.3x260
with : x10, x20
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+ 7x21
8x1+ 5x23
6x1+ 9x2 2
with : x10, x20
Problem 3 (10 Points) Prove that the objective function of the following system assumes its minimum
at an extreme point of , provided a minimum exists and that is bounded.
Minimize : z=CTX
subject to : AX =B
with : X0
Dr. Pushkin Kachroo: pushkin@unlv.edu http://faculty.unlv.edu/pushkin

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Test1 ECG 795 Optimization, Fall Problem 1 (10 Points) Solve the following optimization problem by hand. Moreover, give a graphical solution also.

Minimize : z = 0.04(x 1 − 95)^2 + 0.02(x 2 − 125)^2 subject to : 0. 2 x 1 + 0. 2 x 2 ≤ 20

  1. 8 x 1 + 0. 3 x 2 ≤ 60 with : x 1 ≥ 0 , x 2 ≥ 0

Problem 2 (10 Points) Put the following program in standard form and provide an initial basic feasible solution.

Minimize : z = 25x 1 + 30x 2 subject to : 4 x 1 + 7x 2 ≥ 1 8 x 1 + 5x 2 ≥ 3 6 x 1 + 9x 2 ≥ − 2 with : x 1 ≥ 0 , x 2 ≥ 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 ℑ is bounded.

Minimize : z = CT^ X subject to : AX = B with : X ≥ 0

Dr. Pushkin Kachroo: pushkin@unlv.edu http://faculty.unlv.edu/pushkin