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MIE376 Lec 1b - LP Problems

MIE376 Lec 1b - LP Problems - MIE376 LP Formulation...

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1 MIE376: LP Formulation Problems 1. A drill and a lathe are used exclusively in the manufacture of two products P1 and P2. The time units necessary for each step (drilling and turning) in the manufacture of both products are shown in the table below. P1 P2 Lathe 1 hr 3 hr Drill 1 hr 1 hr Sales profit per unit \$1 \$2 If the lathe and drill are available for a maximum of 16 hrs and 7 hrs respectively, find the maximum weekly profit possible in the manufacturing of these items. 2. U.S. labs manufactures mechanical heart valves from the heart valves of pigs. Different heart operations require valves of different sizes. U.S. labs purchases pig valves from three different suppliers. The cost and size mix of the valves purchased from each supplier are given as follows: Supplier Cost/Valve % large % med. % small 1 512 42 45 13 2 451 32 37 31 3 373 24 22 54 Each month U.S. labs places one order with each supplier. At least 500 large, 300 medium and 300 small valves must be purchased each month. Because of limited availability of pig valves, at most 500 valves per month can be purchased from each supplier. How would you go about finding the best combination? 3. Two investments with varying cash flows are available as follows: Investment Oct. 1, 2011 Oct. 1, 2012 Oct. 1, 2013 Oct. 1, 2014 A (\$6,000) (\$5,000) \$7,000 \$9,000 B (\$8,000) (\$3,000) \$9,000 \$7,000 Any fraction of an investment can be purchased. By Oct. 1, 2011 you will have \$10,000 available for investment, and a year later you will have \$7,000 available. Assuming that the prevailing interest rate is 4% how should the money be used to maximize its Net Present Value. 4. A post office has the following workload: Day of the week S M T W T F S Full time equivalent (FTE) required 11 17 13 15 19 14 16 An FTE represents 8 hrs/day. The post office may meet its daily labour requirements with a combination of full time and part time employees. Both work 5 consecutive days per week. Full-time employees work 8 hrs/day at a rate of \$15/hr, and part time employees work 4 hrs/day at \$10/hr. Agreements with the union limit the composition of part-time labour to 25% of the labour requirements. 5. A company faces the following varying demand and unit production cost for its product over the next three months: Month Oct. Nov. Dec. Demand 20 10 15 Unit Production cost 13 14 15 Because the product is sold throughout each month, assume that only half the goods produced during a month can be sold within that month, the other half is used to meet the demand for the following month. For goods stored in inventory a holding cost of \$2 per unit is assessed against each months ending inventory. At the end of September the company has 5 units on hand. What production schedule meets the demand at minimum overall cost?

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2 6. Priceler manufactures sedans and wagons. The number of vehicles that can be sold each of the next 3 months are shown below.
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