The Omega Manufacturing Company has discontinued the production of a certain unprofitable product line. This act cre- ated considerable excess production capacity. Management is con- sidering devoting this excess capacity to one or more of three prod- ucts; call them products 1, 2, and 3. The available capacity on the machines that might limit output is summarized in the following table: Available Time Machine Type (Machine Hours per Week) Milling machine 500 Lathe 350 Grinder 150 The number of machine hours required for each unit of the re- spective products is Productivity coefficient (in machine hours per unit) Machine Type Product 1 Product 2 Product 3 Milling machine Lathe 3 5 5 4 Grinder 3 2

The Omega Manufacturing Company has discontinued the production of a certain unprofitable product line. This act cre- ated considerable excess production capacity. Management is con- sidering devoting this excess capacity to one or more of three prod- ucts; call them products 1, 2, and 3. The available capacity on the machines that might limit output is summarized in the following table: Available Time Machine Type (Machine Hours per Week) Milling machine 500 Lathe 350 Grinder 150 The number of machine hours required for each unit of the re- spective products is Productivity coefficient (in machine hours per unit) Machine Type Product 1 Product 2 Product 3 Milling machine Lathe 3 5 5 4 Grinder 3 2

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

3.1-11.* The Omega Manufacturing Company has discontinued
the production of a certain unprofitable product line. This act cre-
ated considerable excess production capacity. Management is con-
sidering devoting this excess capacity to one or more of three prod-
ucts; call them products 1, 2, and 3. The available capacity on the
machines that might limit output is summarized in the following
table:
Available Time
Machine Type
(Machine Hours per Week)
Milling machine
Lathe
500
350
Grinder
150
The number of machine hours required for each unit of the re-
spective products is
Productivity coefficient (in machine hours per unit)
Machine Type
Product 1
Product 2
Product 3
Milling machine
Lathe
9
3
5
5
4
Grinder
3

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
Omega should produce to maximize profit.
(a) Formulate a linear programming model for this problem.
c (b) Use a computer to solve this model by the simplex method.

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