For the following problem, solve the linear programming model by using the computer. You must use QM for Windows to solve this problem. Please include the original problem plus results screen in the Word document you create. Follow the format of the examples that were posted in the Doc Sharing tab. Include the model formulation or a window showing the constraints. Save the resulting file as a Word file. Show all work.
1. The Pyrotec Company produces three electrical products- clocks, radios, and toasters. The products have the following resource requirements:
Cost/Unit Labor Hours/Unit
Clock $7 2
Radio 10 3
Toaster 5 2
The manufacturer has a daily production budget of $2,000 and a maximum of 660 hours of labor. Maximum daily customer demand is fo r200 clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios for $20, and toasters for $12. The company wants to know the optimal product mix that will maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
2. The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture- wood, upholstery, and labor. The resource requirements for each piece of furniture and the toal resources available weekly are as follows:
Wood(lb.) Upholstery(yd.) Labor(hr.)
Sofa 7 12 6
Table 5 - 9
Chair 4 7 5
Total available resources 2,250 1,000 240
The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity o f650 pieces of furniture. Each sofa earns $400 in profit, each table, $275, and each chair, $190. The company wants to know how many pieces of each type of furniture to make per week to maximize profit.
a. Formulate a linear programming model for this problem
b. Solve the model by using the computer
3. Green Valley Mills produces carpet at plants i St.Louis and Richmond. The plants ship the carpet to two outlets in Chicago and Atlanta. The cost per ton of shipping carpet from each of the two plants to the two warehouses is as follows:
To
From Chicago Atlanta
ST. Louis $40 $65
Richmond 70 30
The plant at St.Louis can supply 250 tons of carpet per week, and the plant at Richmond can supply 400 tons per week. The Chicago outlet has a demand of 300 tons per week; the outlet at Atlanta demands 350 tons per week. Company managers want to determine the number of tons os carpet to ship from each plant to each outlet in order to minimize the total shippiing cost.
a. Formulate a linear programming model for this problem
b. Solve the model by using the computer.