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Exam1-2007-Solutions-updated

Exam1-2007-Solutions-updated - Decision Modeling and...

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Decision Modeling and Applications MBAC6080, Spring 2007 Instructor: Thomas Vossen Midterm Exam Solutions Score:________ Max: 100 points Name:__________________________________ Instructions: Make sure to sign the honor code pledge ! I cannot accept exams without your signature. For full credit, complete solutions must be provided to all problems. An answer without motivation or explanation is not acceptable. I expect that you clearly organize and format the answers to the solutions . Note: Carefully read the questions before you start working on the solutions. Clearly state your assumptions (if any), and try to keep your solutions as simple as possible. Honor Code Pledge “On my honor, as a University of Colorado at Boulder student, I have neither given nor received unauthorized assistance on this work.” Signature:____________________________
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Question 1 (20pts): Graphical Method Consider the following linear programming problem: Min Z = 3 x 1 - 4 x 2 subject to: 2x 1 - x 2 6 ( C1 ) 10 x 1 + 5 x 2 60 ( C2 ) 2 x 1 + 3 x 2 42 ( C3 ) -2 x 1 + 5 x 2 30 ( C4) x 1 , x 2 0 X 2
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X 1
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On the diagram above: a. Plot and label the constraints (5pts) b. Shade the feasible region (4pts) c. Graph the objective function (4pts)
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d. Identify and label the optimal solution (4pts) e. If the sign of constraint C3 is changed to ≥, what is the effect on the problem? (3pts) Unbounded problem Infeasible problem Multiple optima No change Other … There will be a single solution (which is also optimal that satisfies all constraints) X1=7.5, X2=9
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Question 2(20 pts): LP Formulation CSL is a chain of computer service stores. The number of hours of skilled repair time that CSL requires during the next four months is as follows: Month 1: 6,000 hours Month 2: 7,000 hours Month 3: 9,000 hours Month 4: 10,000 hours At the beginning of the first month, 50 skilled technicians work for CSL. Each skilled
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