Midterm 1 - ENGR62/MS&E111 Introduction to Optimization...

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ENGR62/MS&E111 Spring 2005 Introduction to Optimization May 5, 2005 Prof. Ben Van Roy Midterm Exam: Due Friday May 6th, 2005, at 5:00PM Instructions Sign the honor code statement and return this hand-out when you submit your solutions. Turn in your exam to Prof. Van Roy’s office, Terman 315. The exam will be graded out of total of 100 points. Problems 1–4 are each worth 25 points. The extra credit problem is worth an additional 5 points. Except for Problem 1, partial credit will be awarded for work that is handed in that is relevant and partially solves a problem. Honor Code In recognition of and in the spirit of the Honor Code, I certify that I will neither give nor receive unpermitted aid on this examination and that I will report, to the best of my ability, all Honor Code violations observed by me. Signature: Name:
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1. True or False (25 points) State whether each of the following statements is true or false. For each part, only your answer, which should be one of “True” or “False,” will be graded. Explanations will not be read. For each correct answer, you will receive five points. For each incorrect answer, you will lose two points. No points are assigned or lost for a part unanswered. a) If a linear program has at least one optimal solution and every optimal solution is a vertex of the feasible region, then it has only one optimal solution. b) For a linear program that has M variables and N constraints ( M N ), at most M constraints can be active at a vertex of the feasible region. c) If a linear program has an unbounded feasible region then it has no optimal solution. d) If a linear program has at least one optimal solution then the feasible region must have a vertex that is an optimal solution. e) If the feasible region of a linear program is nonempty and bounded then it must have a vertex that is an optimal solution. 2. Automobile Manufacturing You are the production manager for a manufacturer of three types of automobile spare parts. You must determine a monthly production plan for the coming month. The manufacture of each part requires processing on each of two machines, with the following processing times in hours: Part A B C Machine1 0.02 0.04 0.03 Machine2 0.05 0.03 0.02 Each machine is available 40 hours per month. Each part manufactured will yield a unit profit as follows: Part A B C Profit 100 90 80 The demand for each part as follows: Part A B C Demand 500 500 400
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In particular, we will be unable to sell units produced beyond the demanded quantity.
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