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A bike dealer buys at a wholesale: bikes, scooters and child's saddles. He wants maximum profit.

He buys the bike (x) for 300, the scooter (y) for 1200 and the saddle (z) for 36. A bike takes 0,5$m^2$, a scooter takes $1m^2$ and a saddle takes $0,1m^2$. The profit for a bike is 100, for a scooter 300 and a saddle 20.

  • He'll buy a maximum of 100 bikes and 50 saddles

  • He has $101m^2$ to put all the stuff in.

  • He has $93000$ to buy stuff with.

So I wanted to do this using the wonderful Simplex method, and these are the constraints I've come up with:

$$x \leq 100$$

$$z \leq 50$$

$$0.5x + y + 0.1z \leq 101$$

$$ 300x + 1200y + 36z \leq 93000$$

And $$M = 100x + 300y + 20z$$ Is this correctement?

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That is right. $M$ is the quantity you want to maximize subject to the four constraints above it.

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  • $\begingroup$ If I put this into a matrix, and find its rref I can find the maximum immediately right? $\endgroup$ – Ylyk Coitus Apr 1 '13 at 19:46
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    $\begingroup$ So the maximum profit is 25800; you have to buy 80 bikes, 56 scooters and 50 saddles. I just got it using the rref button on my graphing calculator. Then just figuring out which number belonged to which variable. Thanks for this help. You might not think this help was a lot, but for a self-studying student like me 'that is right' means a lot. $\endgroup$ – Ylyk Coitus Apr 1 '13 at 19:56

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