# Are these constraints correct?

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 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?

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