hw #1 3.1-11 3.4-6 3.4-14 due: 2004-10-11. 3.1-11 the omega manufacturing manufacturing company has...
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HW #1
3.1-11
3.4-6
3.4-14
Due: 2004-10-11
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3.1-11 The Omega Manufacturing Manufacturing Company 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 ore 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(Machine Hours per Week)
500
350
150
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The number of machine hours required for each unit of the respective products is
Productivity coefficient (in machine hours per unit)
Machine Type
Milling machine
Lathe
Grinder
Product 1
9
5
3
Product 3
5
0
2
Product 2
3
4
0
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 $25, respectively, on products 1, 2, and 3. The objective is to determine how much of each product Omega should produce to maximize profit.
(a) Formulate a linear programming model for this problem.
(b) Use a computer to solve this model by the simplex method.
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1 2 Minimize 40 50 ,
subject to
Z x x
3.4-6 Consider the following LP problem:
1 2
1 2
1 2
2 3 30
12
2 20
x x
x x
x x
1 2
and
0, 0.x x
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(a) Use the graphical method to solve the problem
(b) How does the optimal solution change if the objective function is changed to
?
(c) How does the optimal solution change if the third constraint is changed to
?
1 2 40 70Z x x
1 2 2 15x x
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3.4-14 The Metalco company desires to blend a new alloy of 40% tin, 35% zinc, and 25% lead from several available alloys having the following properties.
Alloy1 2 3 4 5
60 25 45 20 50
10 15 45 50 40
30 60 10 30 10
Property
% of tin
% of zinc
% of lead
Cost ($/lb) 22 20 25 24 27
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The objective is to determine the proportions of these alloys that should be blended to produce the new alloy at a minimum cost.
(a) Formulate a linear programming model for this problem.
(b) Use a computer to solve this model by the simplex method.