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1. A manufacturer produces two models of racing bikes, Sport and Town, each of which must be processed through two machine shops. Machine shop 1 is available for 120 hours per month and machine shop 2 for 180 hours per month. The manufacturer of each Sport bike takes 6 hours in machine shop 1 and 3 hours in machine shop 2. The corresponding manufacturing time for the Town bike is 4 hours in machine shop 1 and 10 hours in machine shop 2. If the profit per unit is £180 for the Sport bike and £220 for the Town bike, determine how the manufacturer should arrange production in order to maximize its total monthly profit. What is the maximum monthly profit?
2. (Original post by dshot20)
A manufacturer produces two models of racing bikes, Sport and Town, each of which must be processed through two machine shops. Machine shop 1 is available for 120 hours per month and machine shop 2 for 180 hours per month. The manufacturer of each Sport bike takes 6 hours in machine shop 1 and 3 hours in machine shop 2. The corresponding manufacturing time for the Town bike is 4 hours in machine shop 1 and 10 hours in machine shop 2. If the profit per unit is £180 for the Sport bike and £220 for the Town bike, determine how the manufacturer should arrange production in order to maximize its total monthly profit. What is the maximum monthly profit?
Instinctively, I'd set up some inequalities corresponding to these constraints and look for values that satisfy them all.
You should give the things that have constraints on them letters (e.g x,y etc)

Is there a name for this kind of maths? It's certainly not statistics.

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Updated: April 11, 2013
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