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?