NAME: SCORE: _______________ _______________ Midterm Exam BMDS 3371 This midterm exam is an open book test of your ability to apply the linear programming concepts covered in the first half of this term. You may use notes, any handouts I distributed during class, as well as your textbook to assist you. Collaborative work with others is not permitted. The exam itself is due by 11:59 pm (cst) on Wednesday, November 25th. Exams received after this due date will be assessed a 10% penalty. Please be advised that students are required to submit their linear programs (with sensitivity reports where necessary) and provide direct answers to each part of each exam question. 1. (20 pts.) You are the recently hired Chief Operations Officer at ABC Inc, a regional firm which produces specialized circuit boards used in the production of various makes and models of automobiles. The company currently owns three production plants, one much newer than the other two. Once the circuit boards are produced, the firm ships them to one of four warehouses throughout the state where they are placed in inventory until ordered by the end-user. Each circuit board sells for $150. Being the good COO that you are, you are always looking for ways to minimize costs and increase profitability. You suspect that there is much room for improvement in this regard. Specifically, you have reason to believe that production and stocking levels of each plant and warehouse could be modified to yield the desired results. The details of this managerial challenge are as follows: Production Costs - Plant A -- $100 per circuit board Plant B -- $120 per circuit board Plant C -- $90 per circuit board Plant Capacity - Plant A - 1,200 circuit boards Plant B - 1,200 circuit boards Plant C - 500 circuit boards Demand Forecast - Warehouse #1 - 700 circuit boards Warehouse #2 - 400 circuit boards Warehouse #3 - 600 circuit boards Warehouse #4 - 500 circuit boards 1 Shipping Costs Plant A Plant B Plant C Warehouse #1 $10 $50 $25 Warehouse #2 $15 $20 $45 Warehouse #3 $40 $25 $30 Warehouse #4 $30 $20 $22 Create a linear program that shows exactly how many circuit boards should be produced at each plant and then shipped to each warehouse in order to maximize resulting profits. Your completed model should show the optimal values of all 12 decision variables AS WELL AS the optimal value of the objective function. 2. (20 pts.) Given the following LP model, Minimize (costs) Z = 4X1 + 8X2 Subject to Fiber Protein a.) b.) c.) d.) e.) f.) g.) h.) 5X1 + 8X2 > 40 6X1 + 4X2 > 24 X1, X2 > 0 What is the optimal value of the objective function? What are the optimal values of the two decision variables? Find the range of optimality for each objective function coefficient. How would a decrease of $1 in the X1 coefficient of the objective function affect the optimal values of the decision variables? How would a decrease of $1 in the X1 coefficient of the objective function affect the optimal value of the objective function? What is the dual value (AKA -\"shadow price\") for the RHS of the protein constraint? What is the range of feasibility of the dual value for the RHS of the protein constraint? What impact on total cost would a decrease of 2 units in the RHS of the protein constraint have? Please explain the rationale for your answer. 3. (20 pts.) The manager of FYZ Incorporated has been presented with the following LP model: Minimize (costs) Z = 30A + 45B Subject to 5A + 2B > 100 4A + 8B > 240 B > 20 A and B > 0 2 She would like your assistance with several questions below. a.) b.) c.) d.) e.) f.) g.) h.) What is the proper name of the last constraint shown in the model? What is the optimal value of the objective function? What are the optimal values of the two decision variables? If the cost of B could be reduced to $42 per unit, how many units of B would be optimal? If the cost of B could be reduced to $42 per unit, what would the minimum total cost be? What is the dual value (AKA--\"shadow price\") for the RHS value of the first constraint? What is the range of feasibility for the RHS value of the first constraint? By what amount would the total cost change, and in what direction, if the RHS value of the first constraint was changed to 110? Please explain the rationale for your answer. 3. Your \"Solutions Plus\" case study write-up will constitute the remaining portion (40 points) of your midterm exam. Please keep your response between 2 and 3 pages (double-spaced) in length....not including the associated linear program and sensitivity report you will have to submit in an Excel format. The score will be primarily dependent on the content and accuracy of your responses to the first three sets of issues mentioned in the \"Managerial Report\" on Page 306 of your text. However, part of the evaluative process (10 of 40 points), will involve the overall professionalism of the write-up itself. I expect the work to be free of typographical errors and inclusive of the kind of responses you would be expected to provide to a reporting supervisor. 3 Shipping Costs Warehouse #1 Plant A Plant B Plant C Warehouse #2 $10 $50 $25 Warehouse #3 $15 $20 $45 Cost each circuit board Warehouse #4 $40 $25 $30 $30 $20 $22 $150 Production Costs Plant A Plant B Plant C $100 $120 $90 Plant Capacity Capacity Constraints 700 Plant A Plant B Plant C 1200 0 = $700 Warehouse #2 Warehou se #1 Warehou se #2 Warehou se #3 Warehou se #4 Warehouse #3 $400 = $600 $500 Warehouse #4 $700 = $400 $600 $500 = Profit Warehouse #1 Plant A Plant B Plant C Total Objective Function $40 ($20) $35 $55 $ Warehouse #3 $35 $10 $15 $60 Warehouse #4 $10 $5 $30 $45 Total $20 $10 $38 $68 79,000.00 Warehouse #1 Plant A Plant B Plant C Warehouse #2 Warehouse #2 700 400 0 0 0 3.55271367880E-015 Warehouse #3 Warehouse #4 0 0 600 500 Demand Forcast 500 Demand Constraints Warehouse #1 1200 1200 Plant C 1200 0 Plant A Plant B 0 0 500 $105 $5 $118 $700 $400 $600 $500 Decision Variables x1 x2 Constraints Fiber Protein 8 0 40 48 x1,x2 Objective value 32 40 24 0 Shipping Costs Warehouse #1 Plant A Plant B Plant C Warehouse #2 $10 $50 $25 Warehouse #3 $15 $20 $45 Cost each circuit board Warehouse #4 $40 $25 $30 $30 $20 $22 $150 Production Costs Plant A Plant B Plant C $100 $120 $90 Plant Capacity Capacity Constraints 700 Plant A Plant B Plant C 1200 0 = $700 Warehouse #2 Warehou se #1 Warehou se #2 Warehou se #3 Warehou se #4 Warehouse #3 $400 = $600 $500 Warehouse #4 $700 = $400 $600 $500 = Profit Warehouse #1 Plant A Plant B Plant C Total Objective Function $40 ($20) $35 $55 $ Warehouse #3 $35 $10 $15 $60 Warehouse #4 $10 $5 $30 $45 Total $20 $10 $38 $68 79,000.00 Warehouse #1 Plant A Plant B Plant C Warehouse #2 Warehouse #2 700 400 0 0 0 3.55271367880E-015 Warehouse #3 Warehouse #4 0 0 600 500 Demand Forcast 500 Demand Constraints Warehouse #1 1200 1200 Plant C 1200 0 Plant A Plant B 0 0 500 $105 $5 $118 $700 $400 $600 $500 Decision Variables x1 x2 Constraints Fiber Protein 8 0 40 48 x1,x2 Objective value 32 40 24 0 cynthiakerubo10@gmail.com