If I can sell a chip for 4 dollars and know the marginal cost function for making x chips a day to be C'(x)=4/(√(1+0.04x)) with the limit of having to make fewer than 400 chips, what is the profit for making and selling 200 chips given that I can see each chip for 4 dollars? I also know C(200) is equal to 800 which means I can find any fixed costs and I believe them to be 200 but just am a bit confused on the switching to profit part.

Answer 1

C'(x)=4/(√(1+0.04x))
so the total cost for making x chips is
C(x) = 40√(x+25) + k
since C(200) = 800,
800 = 40*15 + k
k = 200
revenue for selling x is 4x
the profit p(x) = revenue - cost, so
p(200) = 4*200 - 800 = 0

Answer 2

So 200 would be the fixed cost then since it is K?

Answer 3

nevermind I figured it out