Linear programming:
Example:
Suppose a factory want to produce two types of hand calculators, type A and type B.
The cost, the labor time and the profit for every calculator is summarized in the
following table:
Type
Cost
Labor Time
Profit
A
B
$30
$20
1 (hour)
4 (hour)
$10
$8
Suppose the available money and labors are $18000 and 1600 hours. What should the
production schedule be to ensure maximum profit?
[solution:]
Suppose
x1 is the number of type A hand calculators and x2 is the number of
type B hand calculators. Then, we want to maximize
p  10x1  8x2
subject to
30 x  20 y  18000
x  4 y  1600
x  0, y  0
where
p
is the total profit. The above equation and inequality can be transformed
into the following linear system by employing some “dummy” variables,
10 x  8 y  p
0
30 x  20 y  u
 18000
x  4y 
v  1600
x  0, y  0, p  0, u  0, v  0
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