Assignment Requirements
Homework – Week 3
Linear and Nonlinear Programing Models
Instruction.
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
Input
Cost
Density
Viscosity
Sulfur
Light gas oil
$69.50
0.83
40
1.0
Heavy gas oil
$66.70
0.88
26
2.2
Waxy distillate
$56.40
0.92
30
2.8
Atmospheric residue
$16.50
0.97
65
4.1
Vacuum residue
$10.40
1.50
48
5.0
Upper limits
Blending plan (1000s of barrels)
Input
Input used
Available
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
>=
>=
>=
Demand
700
300
150
Total cost
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