Min max: how much of the tax to absorb

[SammyS]

But why:
$$\Pi\prime = x(200-0.01x) - 50x + 20,000 - 0.1x$$
i think it should be:
$$\Pi\prime = x(200-0.01x) - 50x - 20,000 - 10x$$

Yes.
It looks like @MrAnchovy suggests the only change is to include the new 10 cent tax to the cost, $\ y\,.\$ The quantities are all in cents and not dollars or other currency, so that should be an "extra" $\ -10 x\$ upon subtracting $\ y\$ from $\ x P \,.$

Try it.

 

[Karol]

I tried it and it comes right:

Genius

 

[SammyS]

Thanks @MrAnchovy and @tnich .
Now I see the light.

 

[pbuk]

i think it should be:
$$\Pi\prime = x(200-0.01x) - 50x - 20,000 - 10x$$

You are right

The quantities are all in cents and not dollars or other currency

Yes, sloppy of me to miss that, thanks!