Department of Mechanical and Industrial Engineering: Operations Research
NORTHEASTERN UNIVERSITY
Department of Mechanical and Industrial Engineering
Operations Research
Prof. Gupta
OR 6205
Fall 2014
Class Handout No. 1
Problem No. 1. A manufacturing firm has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity.
Management is considering devoting this excess capacity to one or more of three products; call them products 1, 2, and 3. The available capacity on the machines that might limit output is summarized in the following table:
Machine Type
Milling machine
Lathe
Grinder
Available Time (in Machine Hours per Week)
500
350
150
The number of machine hours required for each unit of the respective products is as follows: Machine Type
Milling machine
Lathe
Grinder
Product 1
9
5
3
Product 2
3
4
0
Product 3
5
0
2
The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week.
The unit profit would be $50, $20, and $25, respectively, on products 1, 2, and 3. The objective is to determine how much of each product the firm should produce to maximize profit. Formulate a linear programming model for this problem.
Problem No. 2. A television manufacturing company has to decide on the number of 27and 20-inch sets to be produced at one of its factories. Market research indicates that at most 40 of the 27-inch sets and 10 of the 20-inch sets can be sold per month. The maximum number of work hours available is 500 per month. A 27-inch set requires 20 work hours, and a 20-inch set requires 10 work hours. Each 27-inch set sold produces a profit of $120, and each 20-inch set produces a profit of $80. A wholesaler has agreed to purchase all the television sets produced if the numbers do not exceed the maximum indicated by the market research. Formulate a linear programming model for this problem. Problem No. 3. Solve the following linear programming problem
Department of Mechanical and Industrial Engineering
Operations Research
Prof. Gupta
OR 6205
Fall 2014
Class Handout No. 1
Problem No. 1. A manufacturing firm has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity.
Management is considering devoting this excess capacity to one or more of three products; call them products 1, 2, and 3. The available capacity on the machines that might limit output is summarized in the following table:
Machine Type
Milling machine
Lathe
Grinder
Available Time (in Machine Hours per Week)
500
350
150
The number of machine hours required for each unit of the respective products is as follows: Machine Type
Milling machine
Lathe
Grinder
Product 1
9
5
3
Product 2
3
4
0
Product 3
5
0
2
The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week.
The unit profit would be $50, $20, and $25, respectively, on products 1, 2, and 3. The objective is to determine how much of each product the firm should produce to maximize profit. Formulate a linear programming model for this problem.
Problem No. 2. A television manufacturing company has to decide on the number of 27and 20-inch sets to be produced at one of its factories. Market research indicates that at most 40 of the 27-inch sets and 10 of the 20-inch sets can be sold per month. The maximum number of work hours available is 500 per month. A 27-inch set requires 20 work hours, and a 20-inch set requires 10 work hours. Each 27-inch set sold produces a profit of $120, and each 20-inch set produces a profit of $80. A wholesaler has agreed to purchase all the television sets produced if the numbers do not exceed the maximum indicated by the market research. Formulate a linear programming model for this problem. Problem No. 3. Solve the following linear programming problem