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EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon). Note : (a) Do not send me after copying your computer results of QSB. Answer what are your decision variables, formulation and solution, only. See my HW answer on my HP.

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EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

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  1. EMGT 501 Fall 2005 Midterm Exam Due Day: Oct 17 (Noon)

  2. Note: (a) Do not send me after copying your computer results of QSB. Answer what are your decision variables, formulation and solution, only. See my HW answer on my HP. (b) Put your mailing address so that I will be able to return your exam result via US postal service. (c) Answer on a PPS series of slides. (d) Do not discuss on the exam with other students. (e) Return your answer attached to your e-mail.

  3. 1. Linear Programming (20%) Benson Electronics manufactures three components to produce cellular telephones and other communication devices. In a given production period, demand for the three components may exceed Benson’s manufacturing capacity. In this case, the company meets demand by purchasing the components from another manufacturer at an increased cost per unit. Benson’s manufacturing cost per unit and purchasing cost per unit for the three components are as follows: Source Component 1 Component 2Component 3 Manufacture $4.50 $5.00 $2.75 Purchase $6.50 $8.80 $7.00

  4. Manufacturing times in minutes for Benson’s three departments are as follows: Department Component 1 Component 2Component 3 Production 2 3 4 Assembly 1 1.5 3 Testing and packaging 1.5 2 5 For instance, each unit of component 1 that Benson manufactures requires 2 minutes of production time, 1 minute of assembly time, and 1.5 minutes of testing and packaging time. For the next production period, Benson has capacities of 360 hours in the production department, 250 hours in the assembly department, and 300 hours in the testing and packaging department.

  5. Formulate a linear programming model that can be used to determine how many units of each component to manufacture and how many units of each component to purchase. Assume that component demands that must be satisfied are 6000 units for component 1, 4000 units for component 2, and 3500 units for component 3. The objective is to minimize the total manufacturing and purchasing costs. • What is the optimal solution? How many units of each component should be manufactured and how many units of each component should be purchased? • Show its dual formulation • Discuss complementary slackness condition between the primal and dual models.

  6. 2. Linear Programming (15%) Consider the following problem. Maximize subject to

  7. Solve the problem. • What is B-1? How about B-1b and CBB-1b? • If the right hand side is changed from (5, 4) to (6, 5), how is an optimal solution changed? How about an optimal objective value?

  8. 3. Linear Programming (15%) Suppose that in a product-mix problem x1, x2, x3,and x4 indicate the units of products 1,2,3, and 4, respectively, and we have Max s.t. Machine A hours Machine B hours Machine C hours

  9. Formulate the dual model to this problem. • Solve the dual. Use the dual solution to show that the profit-maximizing product mix is x1=0, x2=25, x3=125, and x4=0. • Use the dual variables to identify the machine or machines that are producing at maximum capacity. If the manager can select one machine for additional production capacity, which machine should have priority? Why?

  10. 4. PERT/CPM (20%) Building a backyard swimming pool consists of nine major activities. The activities and their immediate predecessors are shown. Develop the project network. Activity A B C D E F G H I Immediate Predecessor - - A,B A,B B C D E,G,H D,F Assume that the activity time estimates (in days) for the swimming pool construction project are as follows:

  11. Optimistic Activity Most Probable Pessimistic A B C D E F G H I 5 4 6 9 4 2 8 8 4 6 6 7 10 6 3 10 10 5 3 2 5 7 2 1 5 6 3 • What is an activity schedule? • What is a critical path? • What is the expected time to complete the project? • What is the probability that the project can be completed in 25 or fewer days?

  12. 5. Inventory (15%) Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7200 copies. The cost of one copy of the book is $14.50. The holding cost is based on an 18% annual rate, and production setup costs are $150 per setup. The equipment on which the book is produced has an annual production volume of 25,000 copies. Wilson has 250 working days per year, and the lead time for a production run is 15days. Use the production lot size model to compute the following values:

  13. Minimum cost production lot size • Number of production runs per year • Cycle time • Length of a production run • Maximum inventory • Total annual cost • Reorder point

  14. 6. Inventory (15%) A well-known manufacturer of several brands of toothpaste uses the production lot size model to determine production quantities for its various products. The product known as Extra White is currently being produced in production lot sizes of 5000 units. The length of the production run for this quantity is 10 days. Because of a recent shortage of a particular raw material, the supplier of the material announced that a cost increase will be passed along to the manufacturer of Extra White. Current estimates are that the new raw material cost will increase the manufacturing cost of the toothpaste products by 23% per unit. What will be the effect of this price increase on the production lot sizes for Extra White?

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