Homework – Week 3
Linear and Nonlinear Programing Models
Please create a single Excel file with 2(or 3) worksheets – each problem should be on a separate worksheet (tab).
Problem 1. Problem 4.45 (a) (p. 196) – No template is provided.
A bus company believes that it will need the following numbers of bus drivers during each of the next five years: 60 drivers in year 4; 75 drivers in year 5. At the beginning of each year, the bus company must decide how many drivers to hire or fire. It costs $4000 to hire a driver and $2000 to fire a driver. A driver’s salary is $10,000 per year. At the beginning of year 1, the company has 50 drivers. A driver hired at the beginning of a year can be used to meet current year’s requirements and is paid full salary for the current year. (A) Determine how to minimize the bus company’s salary, hiring, and firing costs over the next five years.
Problem 2. Problem 4.78(a) – p. 201. The required input data is provided in the template below. An oil company produces gasoline from five inputs. The cost, density, viscosity, and sulfur content, and the number of barrels available of each input are listed in the file. Gasoline sells for $72 per barrel. Gasoline can have a density of at most 0.98 units per barrel. A viscosity of at most 37 units per barrel, and a sulfur content of at most 3.7 units per barrel. (A) How can the company maximize its profit?
Problem 4.78(a) – p. 201
Selling price per barrel
Light gas oil
Heavy gas oil
Blending plan (1000s of barrels)
Light gas oil
<= 20 Heavy gas oil <= 30 Waxy distillate <= 20 Atmospheric residue <= 20 Vacuum residue <= 30 Constraints Density Viscosity Sulfur Actual <= <= <= Maximum Profit Problem 3. (Problem 7.45 (a), p. 414) Suppose Ford currently sells 250,000 Ford Mustangs annually. The unit cost of a Mustang, including the delivery cost to a dealer, is $16,000. The current Mustang price is $20,000, and the current elasticity of demand for the Mustang is -1.5. (A). Determine a profit-maximizing price for a Mustang, Do this when the demand function is of the constant elasticity type. Do it when the demand function is linear. a) Do it only for the linear demand function. b) Use DataTable to calculate profits for specified prices and highlight the best profit c) Generate a scatter diagram based on the table created in (b) Problem 7.45 (a) – p. 414 – Pricing a Mustang Current demand 250000 Current price $20,000 Unit cost $16,000 Current elasticity -1.5 Part (a): linear demand a b New price New demand Profit Price Profit $21,000.00 $21,500.00 $22,000.00 $22,500.00 $23,000.00 $23,500.00 $24,000.00 $24,500.00 $25,000.00 $25,500.00 $26,000.00 $26,500.00 $27,000.00 $27,500.00 $28,000.00 $28,500.00 Problem 4 (Optional bonus problem). The required input data is provided in the template below. 7 bonus points will be added to your HW3 grade if your submitted solution is completely correct (i.e., there will be no partial credits for the bonus problem). Aluminaca produces 100-foot-long, 200-foot-long, and 300-foot-long ingots for customers. This week’s demand for ingots is listed in the file. Aluminaca has four furnaces in which ingots can be produced. During one week, each furnace can be operated for 50 hours. Because ingots are produced by cutting up long strips for aluminum, longer ingots take less time to produce than shorter ingots. If a furnace is devoted completely to producing one type of ingot, the number it can produce in one week is listed in the same file. For example, furnace 1 could produce 350 300-foot ingots per week. The material in an ingot costs $10 per foot. A customer who wants 100-foot or 200-foot ingot will accept an ingot of that length or longer. How can Aluminaca minimize the material costs incurred in meeting required weekly demands? Problem 4.101. (p. 205)- Ingot production at Aluminaca Production data (maximum production if furnaces are devoted entirely to a particular ingot length) Furnace 100-foot 200-foot 300-foot 1 230 340 350 2 230 260 280 3 240 300 310 4 200 280 300 Cost per foot Decisions (how many hours on each furnace to devote to each ingot length) Furnace 100-foot 200-foot 300-foot Sum Available 1 <= 2 <= 3 <= 4 <= Ingots produced Furnace 100-foot 200-foot 300-foot 1 2 3 4 Total Demand constraints 100-foot 200-foot 300-foot Available >=
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