# Maximising Profits

• Dec 13th 2009, 10:32 AM
Ife
Maximising Profits
I have a question here that i think i am using the wrong formula. Suppose a business sells x gadgets for p=250 - 0.01x 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 maximise profit.

What i was saying is that the profits would be the difference of the selling price - cost to produce. then i would have had to differentiate and equate to zero... but that's giving me a weird undifferentiable answer ... so i think i am wrong. can i get some direction please?
• Dec 13th 2009, 11:38 AM
nehme007
p is the price per unit. They sell x units at a total cost of c(x). Net profit is then px - c(x) = (250 - 0.01x)x - (1000 + 25x). Should be easy to differentiate.
• Dec 13th 2009, 12:39 PM
Ife
Quote:

Originally Posted by nehme007
p is the price per unit. They sell x units at a total cost of c(x). Net profit is then px - c(x) = (250 - 0.01x)x - (1000 + 25x). Should be easy to differentiate.

i knew there was some multiplication by x involved somewhere. Thanks!