EM680-HW2

OM603 HW2 Linear Models 2.1. Brown Furniture Revisited Revisit the Brown Furniture Company (Example 2.1). As plans are being made for a new quarter, a revised set of figures on resource availabilities is compiled. The new resource limits are as follows. Fabrication hours 2000 Assembly hours 1800 Machining hours 1600 Wood supply 9400 The other data, on profit contributions and resource consumptions, all remain unchanged. (a) What are the optimal production quantities of chairs, desks, and tables? (b) What is the maximum profit contribution? (c) Which constraints are binding in the optimal solution? (d) Which scarce resource is the most valuable? (ie: if raised by one unit, which constraint raises the profit most? What is the value of that unit increase? 2.2 Diner Staffing Alex's Diner serves food from 6am until midnight. The need for wait staff fluctuates during each day, but day-to-day differences can be ignored when plans are being made. The fluctuations are described by the table below, which displays the number of wait staff needed for each hour. Start Time 6am 7am 8am 9am 10am 11am noon 1pm 2pm Needed 4 5 5 6 4 4 8 8 6 Start Time 3pm 4pm 5pm 6pm 7pm 8pm 9pm 10pm 11pm Needed 5 3 5 7 6 5 3 2 2 Each employee on the wait staff works eight hours with a meal break of one hour. (That break must come after at least four hours but no more than five hours of work.) a) What is the minimum staff size needed to cover all of the hourly requirements? b) Highlight the time periods that are overstaffed. 2.3 Production Planning for Automobiles The Auto Company of America (ACA) produces four types of cars: subcompact, compact, intermediate, and luxury. ACA also produces trucks and vans. Vendor capacities limit total production capacity to at most 1,200,000 vehicles per year. Subcompacts and compacts are built together in a facility with a total annual capacity of 620,000 cars. Intermediate and luxury cars are produced in another facility with capacity of 400,000; and the truck/van facility has a capacity of 275,000. ACA’s marketing strategy requires that subcompacts and compacts must constitute at least half of the product mix for the four car types. Profit margins, market potential, and fuel efficiencies are summarized below. Type Profit margin ($/vehicle) Potential sales (in 000s) Fuel efficiency (MPG) Subcompact 150 600 40 Compact 225 400 34