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Practice_Midterm - MATH 164 Optimization Spring 2010...

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MATH 164 Optimization, Spring 2010, Practice midterm Notes: The actual midterm is on Wednesday, May 5, 2010 1:00 pm - 1:50 pm MS 5127 (the usual lecture room). The midterm is a closed-book and closed-note examination. Calculators are not allowed, but one 5x7 index card is permitted. However it is more important to understand the concepts rather than just write down the formulas in your card. You will probably not have enough time to constantly look up your index card during the exam. The practice midterm contains more problems than the actual one. Problem 1 : Consider the linear programming: Minimize z = - x 1 - 2 x 2 , subject to x 1 + x 2 1 - x 1 + 2 x 2 6 2 x 1 - x 2 ≥ - 2 x 1 , x 2 0 . (a) Show that ¯ x = (0 , 2) T is a feasible point to the problem and label each of the constraints as active or inactive. (b) Show that p = (2 , 1) T is a feasible direction for the point ¯ x = (0 , 2) T . (c) Among those feasible directions of the point ¯ x = (0 , 2) T , what are the descent directions (if any)?
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