LINEAR PROGRAMMING an example Pamela Leutwyler.

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LINEAR PROGRAMMING an example Pamela Leutwyler

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 + 5y < = 60 Space for x rabbits + space for y chicks = 48 4x + 1y < = 48 x = # rabbits and y = # chickens

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. 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.