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mt.f09

# mt.f09 - CO 350 Linear Optimization Fall 2009 Midterm...

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Unformatted text preview: CO 350 Linear Optimization Fall 2009 Midterm Examination October 28 7:00 – 9:00 p.m. Instructions • Print your name, and student identification number SURNAME FIRST NAME STUDENT IDENTIFICATION NUMBER • Check-mark the circle next to your Section number. circlecopyrt LEC 001, J.Cheriyan, TR 10-11:20 circlecopyrt LEC 002, W.H.Cunningham, MWF 10:30-11:20 • There are 10 pages including this cover page. Make sure that you have a complete copy. • You may use results from the course without proof, except for questions that forbid this explicitly. • Calculators are NOT allowed. When solving a computational question, show all of your work. • If you require more space to present your solution, please use the back of the previous page. Indicate clearly where your solution continues. Question Value Mark Question Value Mark 1 6 5 13 2 13 6 11 3 16 7 11 4 14 8 16 Subtotal 49 Subtotal 51 Total 100 1. [6 marks] Convert the following LP problem to standard inequality form. ( P ) maximize x 1 + x 2 + x 3 + x 4 + 100 subject to 2 x 1 − x 2 + 4 x 3 ≤ − 10 x 2 − 5 x 3 + x 4 ≥ − 20 − x 1 − 3 x 3 + 4 x 4 = − 30 x 1 , x 3 , x 4 ≥ 2. [13 marks = 4+3+3+3] (a) Write down the dual problem of the following LP problem: [4] ( P ) maximize z = x 1 − x 2 subject to − 3 x 1 + x 2 ≤ 15 x 1 − 11 x 2 ≤ 10 x 1 , x 2 ≥ (b) Is ˆ x = [10 , 0] T a feasible solution of ( P )? Briefly justify your answer.)?...
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mt.f09 - CO 350 Linear Optimization Fall 2009 Midterm...

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