Maximum Profit

[baumgbr]

Need help with this one. Not sure what the first equation means:

Suppose a business can sell x gadgets for p =250 -.01x dollars apiece, and it costs the business c(x) = 1000 +25x dollars to produce the x gadgets. Determine the production level and cost per gadget required to maximize profit.

What I understand is that if you set marginal cost and marginal revenue equal to each other, then you get maximum profit. I'm not sure what the first equation is. I've assumed it's a revenue equation and then taken it's derivative, but of course you can set it equal to marginal cost and get an equation that makes sense.

I've also assumed that it's the equation for profit, and tried to figure out the revenue equation from there, and their derivatives still didn't do anything for me. What am I missing out on here? Thanks.

 

[baumgbr]

OK. So just to be clear:

First I got:
c'(x) and r'(x)=25=.01
then I tried to get a revenue eqn
r(x) = 1250+24.99x

then got c'(x)=r'(x) =24.99=25

Now I am stuck.

 

[wjm11]

Suppose a business can sell x gadgets for p =250 -.01x dollars apiece, and it costs the business c(x) = 1000 +25x dollars to produce the x gadgets. Determine the production level and cost per gadget required to maximize profit.

Please check your problem statement for accuracy -- checking all signs and, in particular, making sure you didn't switch the "price" and "cost" equations. It does not appear possible to earn a profit with the equations you've presented. Note: I believe that "price" means "revenue." Profit will equal price minus cost. Also, the equations are "per unit" prices and costs.

 

[galactus]

Revenue is how many sold times the price each.

It looks like the revenue would be \(\displaystyle x(\frac{-1}{100}x+250)\)

Profit = Revenue - Cost