Question

TR= 440Q-3Q^2
TC=14Q+225. Find max profit?

Answer 1

I think you need to find the marginal cost (MC) and marginal revenue (MR) of the two formulas. To maximize profits, MC=MR. You get the marginals by differentiating.

SO

MR= 440-6q
MC= 14

Then

440-6q=14
440-14=6q
426=6q
71=q

So then the max output is 71 and then the profit output will be TR-TC

So

X= 440Q-3Q^2-14Q-225
X= 426q - 3q^2 - 225
X=30246 - 15348
X=14898

So mazimum profit is 14898.