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4.1 Problem Set
101
MAXIMIZATION BY THE SIMPLEX METHOD
Solve the following linear programming problems using the simplex method.
1)
Maximize
z
=
x
1
+
2x
2
+
3x
3
subject to
x
1
+
x
2
+
x
3
12
2x
1
+
x
2
+ 3x
3
18
x
1
, x
2
, x
3
0
2)
Maximize
z
=
x
1
+
2x
2
+
x
3
subject to
x
1
+
x
2
3
x
2
+
x
3
4
x
1
+
x
3
5
x
1
, x
2
, x
3
0
3)
A farmer has 100 acres of land on which she plans to grow wheat and corn.
Each acre of wheat requires 4
hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital.
The
farmer has at most 800 hours of labor and $2400 of capital available.
If the profit from an acre of wheat is
$80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?
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4.1 Problem Set
Name:_________________________________
4)
A factory manufactures chairs, tables and bookcases each requiring the use of three operations: Cutting,
Assembly, and Finishing.
The first operation can be used at most 600 hours; the second at most 500 hours;
and the third at most 300 hours.
A chair requires 1 hour of cutting, 1 hour of assembly, and 1 hour of
finishing; a table needs 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing; and a bookcase
requires 3 hours of cutting, 1 hour of assembly, and 1 hour of finishing.
If the profit is $20 per unit for a
chair, $30 for a table, and $25 for a bookcase, how many units of each should be manufactured to maximize
profit?
5).
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 Spring '10
 asda

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