Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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A company manufactures three products 1, 2, and 3. Each product requires production time in three
departments as shown below:
PRODUCT DEPARTMENT 1 DEPARTMENT 2 DEPARTMENT 3
1
3 hr/unit
2 hr/unit
1 hr/unit
2
4 hr/unit
1 hr/unit
3 hr/unit
3
2 hr/unit
2 hr/unit
3 hr/unit
There are 500, 400, and 300 hours of production time available in the three departments, respectively. If
products 1, 2, and 3 contribute $3, $4, and $2.5 per unit to profit, answer the following questions:
(You may attach your solution or write in the box)
a)
Define the decision variables (2 marks).
b)
Write all constraints (3 marks).
c)
Write the objective function (define whether it is a maximization or minimization) (1.5 marks)
A company produces 1,000 refrigerators a week at three plants. Plant A produces 350 refrigerators a week, plant B produces 250 refrigerators a week, and plant C produces 400 refrigerators a week. Production records indicate that 5% of the refrigerators produced at plant A will be defective, 3% of those produced at plant B will be defective, and 7% of those produced at plant C will be defective. All the refrigerators are shipped to a central warehouse. If a refrigerator at the warehouse is found to be defective, what is the probability it was produced at plant A? Show your work
The Livewright Medical Supplies Company has a total of 12 salespeople it wants to assign to
three regions-the South, the East, and the Midwest. A salesperson in the South earns $600 in
profit per month for the company, a salesperson in the East earns $540, and a salesperson in
the Midwest earns $375. The southern region can have a maximum assignment of five sales-
people. The company has a total of $750 per day available for expenses for all 12 salespeople.
A salesperson in the South has average expenses of $80 per day, a salesperson in the East has
average expenses of $70 per day, and a salesperson in the Midwest has average daily expenses
of $50. The company wants to determine the number of salespeople to assign to each region
to maximize profit.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.
Chapter 7 Solutions
Operations Research : Applications and Algorithms
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