1. LINEAR PROGRAMMING
an example
Pamela Leutwyler

2. x = # rabbits and y = # chickens
A farmer raises rabbits and chickens. He can handle no more than 15 animals. A rabbit costs $2 and requires 4 square yards of space. A chicken costs $5 and requires 1 square yard of space. He has a total of $60 and 48 square yards. How many of each should he raise if the profit on a rabbit is $10 and the profit on a chicken is $8?
Total # animals = 15
x + y <= 15
Cost of x rabbits + cost of y chickens = 60
2x y < = 60
Space for x rabbits + space for y chicks = 48
4x + 1y < = 48
x = # rabbits and y = # chickens

3. 4x + y <= 48
x + y < = 15
2x + 5y < = 60
Profit is $10 per rabbit; $8 per chick
$96
$130
$142
$120
( 0 , 12 )
( 5, 10 )
( 11, 4 )
( 12, 0 )

4. The maximum profit is gained by raising 11 rabbits and 4 chicks.
4x + y <= 48
x + y < = 15
2x + 5y < = 60
Profit is $10 per rabbit; $8 per chick
$96
$130
$142
$120
( 0 , 12 )
( 5, 10 )
( 11, 4 )
( 12, 0 )
The maximum
profit is gained
by raising
11 rabbits and
4 chicks.