Problem Set # 1
Problem Set # 1 Due 16.12.08 • Formulate each problem as a linear program • Solve using Excel Solver • Explain the solution. 1. Overtime planning Hartman Company is trying to determine how much of each of two products should be produced over the coming planning period. Shown below is information concerning labor availability, labor utilization, and product profitability: Profit/unit Dept. A hours/unit Dept. B hours/unit Dept. C hours/unit Product 1 Product 2 $30.00 1.00 0.30 0.20 $15.00 0.35 0.20 0.50 Labor Available ----100 hours 36 hours 50 hours Develop a linear programming model of the Hartman Company problem. 2. Quality assurance Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows: Bean 1 2 3 Cost/Pound $0.50 $0.70 $0.45 Available Pounds 500 600 400 Consumer tests with coffee products were used to provide ratings on a 0-to-100 scale, with higher ratings indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows: Bean 1 2 3 Aroma Rating 75 85 60 Taste Rating 86 88 75 It can be assumed that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the blend. Develop a linear programming model of the Hilltop Coffee Company problem assuming they must manufacture 1000 pounds of coffee. 3. Cutting stock The Ferguson Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 1½, 2½, and 3½ inches. The production process provides 200-foot rolls in 10-inch widths only. The firm must therefore cut the rolls to the desired final product sizes. The seven cutting alternatives and the amount of waste generated by each are as follows: Cutting Alternative 1 2 3 4 5 6 7 Number of Rolls 1½ in 2½ in 3½ in 6 0 0 0 4 0 2 0 2 0 1 2 1 3 0 1 2 1 4 0 1 Waste (inches) 1 0 0 ½ 1 0 ½ The minimum requirements for the three products are as follows: Roll Width (inches) 1½ 2½ 3½ Units 1000 2000 4000 Develop a linear programming model of the Ferguson Paper Company problem. 4. Equipment Acquisition The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by trucks. The company has recently received a contract to begin supplying gasoline distributors in southern Ohio and has $600,000 available to spend on the necessary expansion of its fleet of gasoline tank trucks. Three models of gasoline tank truck are available: Truck Model Super Tanker Regular Line Econo-Tanker Capacity (gallons) Purchase Cost Monthly Operating Cost, Including Depreciation 5000 2500 1000 $67,000 $55,000 $46,000 $550 $425 $350 The company estimates that the monthly demand for the region will be 550,000 gallons of gasoline. Due to the size and speed differences of the trucks, the different truck models will vary in terms of the number of deliveries or round trips possible per month. Trip capacities are estimated at 15 trips per month for the Super Tanker, 20 trips per month for the Regular Line, and 25 trips per month for the Econo-Tanker. Based on maintenance and driver availability, the firm does not want to add more than 15 new vehicles to its fleet. In addition, the company has decided to purchase at least three of the new Econo-Tankers to use on the short-run low-demand routes. As a final constraint, the company does not want more than half of the new models to be Super Tankers. Develop a linear programming model of the Two-Rivers Oil Company problem.