# Linear Programming

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#1
Two machines, M1 and M2, are used to make two types of lamp, L1 and L2.
Lamp L1 requires the use of machine M1 for two minutes and machine M2 for 3 minutes. Lamp L2 requires the use of machine M1 for 4 minutes and machine M2 for 3 minutes. The profit on lamp L1 is £7 and the profit on lamp L2 is £11.
Show how can the profit per hour be maximised by formulating the problem.

I got the method right but had problem by finding the constraints the answer say the constraints are 2x+4y<=60 , x,y>=0 , 3x+3y<=60 only but I see that this is only considering the use of the same machine to make each lamp, the question doesn't say he has to use 1 type of machine for each lamp.
So I myself have 2x+3y<=60 assuming that he uses M1 for L1 and M2 for L2, 3x+4y<=60 assuming that he uses M2 for L1 and M1 for L2 (whereas question only uses M1 for L1 and M1 for L2, M2 for L1 and M2 for L2) only so am I wrong by adding 2x+3y<=60
and 3x+4y<=60 ?
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7 years ago
#2
(Original post by Merdan)
I got the method right but had problem by finding the constraints the answer say the constraints are 2x+4y<=60 , x,y>=0 , 3x+3y<=60 only but I see that this is only considering the use of the same machine to make each lamp, the question doesn't say he has to use 1 type of machine for each lamp.
Puzzled. The question says each lamp requires both machines; time on M1 and time on M2.

First constraints arises from the time available on M1, and the second main constraint arises from the time available on M2.

Hence their solution.
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