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IELM202
Exercises
1/6/2011
1.
Zales Jewelers uses rubies and sapphires to produce two types of rings. A type 1 ring
requires 2 rubies, 3 sapphires, and 1 hour of labor. A type 2 ring uses 3 rubies, 2
sapphires, and 2 hours of labor. Each type 1 ring sells for $400, and types 2 ring sells for
$500.
At present, Zales has 100 rubies, 120 sapphires, and 70 hours of labor. Extra
rubies can be purchased at a cost of $100 per ruby.
Market demand requires that the
company produce at least 20 type 1 rings and at least 25 type 2 rings.
The goal is to
maximize profit.
To make an LP formulation, we have defined the following variables:
X1 = type 1 rings produced
X2 = type 2 rings produced
R
= number of rubies purchased
(I) Formulate the LP to maximize the profit:
Max
Z= 400X1 + 500X2 – 100R
s.t.
2X1 + 3X2  R ≤ 100
(1)
3X1+2X2
≤
120
(2)
X1+2X2 ≤
70
(3)
X1
≥ 20
(4)
X2
≥ 25
(5)
X1,X2, R ≥0
(II) Given the partial output of Excel Solver, answer the following question:
Final
Reduced
Objective
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 Fall '10
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