| Finite Math |
Test #1
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Oct. 9, 2000
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| A Track |
R. Hammack
|
|
| Name: ________________________ |
Score: _________
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(1) Multiply the matrices.
| [ |
1
|
3
|
] | [ |
0
|
1
|
2
|
] | = | ||||
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7
|
1
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-5
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2
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5
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(2) Sketch the solutions of the following system of inequalities.
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2x1
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+
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x2
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≤
|
6 |
|
x1
|
+
|
x2
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≤
|
4 |
|
x1
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≥
|
0 | ||
|
x2
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≥
|
0 |
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(3)
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Maximize subject to ...
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P = x1 + x2
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You may use any method. (However, notice that you sketched the feasible region in the previous problem. Feel free to use that information to solve this problem.)
(4) Use Gauss-Jordan Elimination to solve the following system of equations:
|
2x1
|
+
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2x2
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+
|
x3
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=
|
9
|
|
2x1
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+
|
x2
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+
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2x3
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=
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11
|
|
x1
|
+
|
x2
|
+
|
x3
|
=
|
6
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(5) Use the simplex method to solve the following problem.
A hippie farmer wants to sell three crops -- apples, beans, and corn -- at the local Farmer's Market. He reckons it will take him 1 hour to harvest each bushel of apples, 2 hours to harvest each bushel of beans, and 1 hour to harvest each bushel of corn. Each bushel of apples weighs 20 pounds, each bushel of beans weighs 10 pounds, and each bushel of corn weighs 5 pounds. Apples sell for $15 per bushel, beans sell for $10 per bushel, and corn sells for $4 per bushel. He has a maximum of 40 hours in which to harvest the crops. Given that his aging pick-up truck can haul at most 1000 pounds of produce, how many bushels of apples, beans, and corn should he take to the Farmer's Market to realize a maximum profit? (Assume he sells everything he brings to the market.)