Calculus - min & max problem?

A company that produces electronic components can model its revenue and expense by the functions R(x) = 125 / (x^2 - 12x + 61) and E(x) = sq rt(2x+1) +3, respectively, where x is hundreds of components produced and R(x) and E(x) are in thousands of dollars. Assuming 0 ≤ x ≤ 10, answer the following.

a) To the nearest dollar, what is the maximum revenue? (I found this to be $9,000.)

b) If profit is calculated as the difference between revenue and expense, P(x) = R(x) - E(x), how many items should be produced to maximize profit?

I'm stuck with b.

Question

Calculus - min & max problem?

A company that produces electronic components can model its revenue and expense by the functions R(x) = 125 / (x^2 - 12x + 61) and E(x) = sq rt(2x+1) +3, respectively, where x is hundreds of components produced and R(x) and E(x) are in thousands of dollars. Assuming 0 ≤ x ≤ 10, answer the following.

a) To the nearest dollar, what is the maximum revenue?  (I found this to be $9,000.)

b) If profit is calculated as the difference between revenue and expense, P(x) = R(x) - E(x), how many items should be produced to maximize profit?

I'm stuck with b.

anonymous · Answer

to maximize profit, do I just need to find the minimum of E(x) since I have already found the maximum of R(x)? I tried finding the minimum of E(x), but it doesn't seem to work out... I get x=-1/2 for my critical number, which doesn't work because it's outside the domain range.