Summer 2006 first exam - OR 22 FIRST QUIZ(40 1 SUMMER 2006...

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OR 22 SUMMER 2006 FIRST QUIZ May 25, 2006 (40) 1. Julie Lamberth, Operations Manager for the Mebane, NC, unit of the giant German glove manufacturer, Handschuh GmbH, is trying to determine her optimal weekly production schedule. The factory in Mebane has the capability to produce men’s, women’s, and children’s gloves, all of which are made from the same type of top-grain leather. The factory has a long-term supply contract which guarantees delivery of up to 5000 square feet of leather each week. Julie has access to full-time unionized workers who put in 40-hour weeks and are paid $18 per hour. In addition, she can hire part-time, nonunion workers, who put in 20-hour weeks and are paid $10 per hour. Handschuh’s contract with the Amalgamated Leather Workers of America (ALWA) specifies that Julie must employ at least 30 full-time employees at all times and that she must hire at least two full-time employees for each part-time, nonunion employee. The German corporate office has told Julie to produce at least 3000 pairs of gloves per week, in any mixture of men’s, women’s, and children’s. The table below gives various per/pair information about glove production. The gross profit figure includes all costs, except labor . Glove type Leather (square feet) Labor ( minutes ) Gross profit (dollars Men’s 2.0 30 8 Women’s 1.5 45 10 Children’s 1.0 42 6 (27) A. Formulate a linear program (ignoring obvious integrality issues!) to help Julie determine how many workers to hire and how many gloves to produce if she wishes to maximize her profit. Be sure to define all decision variables (including units) and to identify the sources of the constraints. NOTE : If you cannot figure out the decision variables, I’ll sell them to you for 4 points. The remaining questions present changes to the original scenario. For each of them, explain how to change your LP to take the new information into account. You don’t have to rewrite the entire formulation. Just indicate the changes. Questions (B) through (D) are to be answered independently of each other. ( 4) B. At least 15% of the weekly output is to be children’s gloves. ( 3) C. No more than 90% of the total labor wages can be spent on full-time workers ( 6) D. A new leather supplier has appeared on the market and is willing to sell Julie up to 2000 square feet of leather per week, at a price that is $1.50 more per square foot than the price charged by Julie’s current supplier.
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