1
IE 220
Fall 2007
Professor Snyder
October 4, 2007
Name:
MidTerm Exam 1
INSTRUCTIONS:
•
Write neatly and show your work for each question.
•
I will give partial credit for partial answers.
•
You may
not
use your notes, slides, or textbook.
•
You
may
use a calculator.
•
The exam contains a few
Fail Safes
. If you cannot solve a problem whose solution is required
to complete the subsequent problems, you may opt instead to use the Fail Safe as the solution
to the problem. The solutions speciﬁed by the Fail Safes are
incorrect
, but you may proceed
as though they are correct. I will still give partial credit for the incorrect answer that you
provided for the earlier question.
•
If you need more space, use the back of the page or come see me and I will give you more
paper.
•
You may remove the staple if you wish. Please put the pages back in the correct order at the
end of the exam.
•
There are 100 total points.
•
Good luck!
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1. (
46 points
) Dorwyn Glass has won the contract to supply doors and windows for the new
Sands Casino in Bethlehem. Since casinos typically have very few windows, we’ll concentrate
on doors in this problem.
To manufacture hardware (handles, hinges, etc.) for the doors, Dorwyn blends three metals
to form an alloy (a mixture of metals). The table below lists the density, the carbon and
phosphorus content, and the price per kg, of each of the three metals.
The characteristics of the alloy are all proportional to the amount of the three metals. For
example, if the alloy is composed of 20% metal 1, 30% metal 2, and 50% metal 3, then it has
a density of 0
.
2
×
6000+0
.
3
×
5500+0
.
5
×
7000 = 6350, a carbon content of 18%, and a price
of $1.90.
Metal Density Carbon (%) Phosphorus (%) Price ($/kg)
1
6000
20
5
$2.00
2
5500
30
1
$2.50
3
7000
10
6
$1.50
To meet design speciﬁcations, the resulting alloy must satisfy certain requirements:
•
The density must be at most 6000.
•
The carbon content must be at least 25%.
•
The phosphorus content must be exactly 5%.
Let
x
i
represent the percentage of the alloy that is composed of metal
i
,
i
= 1
,
2
,
3. For
example, if
x
2
= 0
.
3, then 30% of the alloy is made up of metal 2.
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 Spring '07
 Storer
 Linear Programming, Optimization, Mathematical optimization, Professor Snyder

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