Download 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.