Practice Midterm I
In order to get the most out of this practice exam you should take it in a timed environment where
you are not using a textbook, your notes, or a calculator. Good luck!
1. Suppose that the financial advisor of a universitys endowment fu

Quiz 4
Name:
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March 31, 2014
1. Provide (with a complete explanation) an upper bound on the optimal value for
the following linear program:
maximize
subject to
z = 2x1 + x2 + 3x3 + 4x4
4x1 + 2x2 + x3 + 5x4 10,
x1 + 3x2 + x3 + 3x4 15,
x1 2x2 +

Quiz 3
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February 19, 2014
1. Consider the following linear program:
maximize
subject to
= x 3y + 4z
2x + 5y + 5z 20
4x + 2y + z 8
x 0, y 0, z 0
(a) Introduce slack variables to create an equivalent linear program in canonical form.
(b)

Quiz 1
January 29, 2014
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Name:
1
1
2
5
3
5
1
Let A = 2 3 8 4 , B = 11 , and C =
2
1
1
3
1
6
0
1. Compute 2A BC T .
2. Solve the system of linear equations given by A~x = B.
1
.

Practice Midterm I Solutions
1. Let x be the amount of money invested in bond AAA and let y be the amount of money
invested in stock BB. Then the resulting linear program is:
Maximize
Subject to
z = 0.07x + 0.09y
x + y = 100, 000
y 30, 000
x 2y
x, y 0
2.

Practice Midterm II
In order to get the most out of this practice exam you should take it in a timed environment where
you are not using a textbook, your notes, or a calculator. Good luck!
1. Give the dual program for the linear program:
Maximize
subject

Quiz 2
Name:
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February 12, 2014
1. A coffee packer blends Brazilian coffee and Colombian coffee to prepare two products:
Super and Deluxe brands. Each kg of Super coffee contains 0.5 kg of Brazilian coffee
and 0.5 kg of Colombian coffee, wher