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MGT 3410 Examination II Spring 2015 Answer all questions (take-home examination) Academic Honesty Policy: I understand that this is an open booksotes exam and I may use a computer to perform computations as necessary. I have neither given nor received help on this exam. Due Date: Apr 22 by 11:59pm Submit your solution electronically in a folder called \"Examination II\" under Dropbox on D2L. sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 1. Consider the following problem with three decision alternatives and three states of nature with the following payoff table representing profits: Decisions d1 d2 d3 States of Nature S1 S2 S3 4 4 -2 0 3 -1 1 5 -3 a. What is the optimal decision if the decision maker is optimistic? (5 points) b. What is the optimal decision if the decision maker is pessimistic? (5 points) c. What is the optimal decision using the minimax regret approach? (5 points) d. If the probabilities that S1, S2, and S3 will occur are 0.2, 0.5, and 0.3, respectively, what is the optimal decision? (5 points) e. Given the information in (d), what is EVPI? (5 points) Th 2. A small company will be introducing a new line of lightweight bicycle frames to be made from special aluminum and steel alloys. The frames will be produced in two models, deluxe and professional, with anticipated unit profits if $10 and $15, respectively. The number of pounds of aluminum alloy and steel alloy needed per deluxe frame is 2 and 3, respectively. The number of pounds of aluminum alloy and steel alloy needed per professional frame is 4 and 2. A supplier delivers 100 pounds of the aluminum alloy and 80 pounds of steel alloy weekly. Develop a linear programming model to determine the weekly production schedule so that the total profit can be maximized. You do not need to solve the model. (10 points) https://www.coursehero.com/file/11754200/Exam-2/ 3. Consider the following linear programming problem: Max s.t. 50 x1 34 x 2 10 x1 7 x 2 49 x1 x 2 5 x1 , x 2 0 Write the problem in standard form. Identify slack/surplus variables. (5 points) b. Identify the feasible region and find the optimal solution. (10 points) c. What are the values of the slack and surplus variables at the optimal solution? (5 points) sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m a. 4. Consider the following linear programming problem: Max s.t. 5x1 5x2 x1 100 x2 80 2 x1 4 x2 400 x1 , x 2 0 a. Identify the feasible region. (7 points) b. Find all the extreme points -- list the value of x1 and x2 at each extreme point. (8 points) c. What is the optimal solution? (5 points) Th 5. Consider the following linear programming problem: Min s.t. 6 x1 9 x2 ($ cost) x1 2 x2 8 10 x1 7.5x2 30 x2 2 x1 , x 2 0 a. Solve this problem using Excel Solver. Provide answer report and sensitivity report. (5 points) https://www.coursehero.com/file/11754200/Exam-2/ b. What is the optimal solution including the optimal value of the objective function? (5 points) c. How much can the unit cost of x2 be decreased without concern for the optimal solution changing? (5 points) d. If simultaneously the cost of x1 was raised to $7.5 and the cost of x2 was reduced to $6, would the current solution still remain optimal? (5 points) Th sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m e. If the right-hand side of constraint 3 is increased by 1, what will be the effect on the objective function value? What is the new objective function value? (5 points) https://www.coursehero.com/file/11754200/Exam-2/ Powered by TCPDF (www.tcpdf.org)