Homework 4

HOMEWORK 4 Use the shells as the basis for solving the problems. Submit the workbook via Canvas by the assigned due date. 1. In the post office example in the text, suppose that each full-time employee works 8 hours per day. Thus, Monday’s requirement of 17 workers can be viewed as a requirement of 8(17) = 136 hours. The post office can meet its daily labor requirements by using both full-time and part-time employees. During each week a full-time employee works 8 hours a day for 5 consecutive days, and a part-time employee works 4 hours a day for 5 consecutive days. A full-time employee costs the post office $15 per hour, whereas a part-time employee (with reduced fringe benefits) costs the post office only $10 per hour. Union requirements limit total part-time labor hours per week to 25% of total hours available per week. Develop a linear model and use Solver to minimize the post office’s weekly labor costs. Then use SolverTable to determine how a change in the part-time labor limitation (currently 25%) influences the optimal solution. Let the part-time labor requirement vary from 10% to 60% in increments of 5%. Let the table show cost of full-time workers , cost of part-time workers , and total cost as the part-time labor requirement varies. 2. During the next 2 months General Cars must meet (on time) the following demands for trucks and cars: month 1, 400 trucks and 800 cars; month 2, 300 trucks and 300 cars. During each month at most 1000 vehicles can be produced. Each truck uses 2 tons of steel and each car uses 1 ton of steel. During month 1, steel costs $400 per ton; during month 2, steel costs $600 per ton. At most 2500 tons of steel can be purchased each month. (Steel can be used only during the month in which it is purchased.) At the beginning of month 1, 100 trucks and 200 cars are in inventory. At the end of each month, a holding cost of $150 per vehicle is assessed. Each car gets 20 mpg, and each truck gets 10 mpg. During each month, the vehicles produced by the company must average at least 16 mpg. Develop a linear model to determine how to meet the demand and mileage requirements at minimum total cost. Now check how sensitive the total cost is to the 16 mpg requirement by creating a table letting the requirement vary from 16 mpg to 18 mpg in increments of .25 mpg, Explain intuitively what happens when the requirement is greater than 17 mpg. 3. The Deckers Clothing Company produces shirts and pants. Each shirt requires 2 square yards of cloth, and each pair of pants requires 3 square yards of cloth. During the next 2 months the following demands for shirts and pants must be met (on time): month 1, 1000 shirts and 1500 pairs of pants; month 2, 1200 shirts and 1400 pairs of pants. During each month the following resources are available: month 1, 9000 square yards of cloth; month 2, 6000 square yards of cloth. (Cloth that is available during month 1 and is not used can be used during month 2.) During each month it costs $4 to make an article of clothing with regular-time labor and $8 with overtime labor. During each month a total of at most 2500 articles of clothing can be produced with regular-time-labor, and an unlimited