Question

The cost function for a product is C(q)=q^3−63q^2+1323q+920 for 0≤q≤50 and a price per unit of $515.
Round your answers to the nearest whole number.

a) What production level maximizes profit?
q =

b) What is the total cost at this production level?
cost = $

c) What is the total revenue at this production level?
revenue = $

d) What is the total profit at this production level?
profit = $

Answer 1

revenue is price * quantity, so
r(q) = 515q
profit = revenue - cost, so
p(q) = 515q - (q^3−63q^2+1323q+920)

(a) where does p'(q) = 0?
(b) c(q) where q is the solution to (a)
(c) and (d) should be clear

Answer 2

I got all except C. That is the only one I am struggling with.
A) q=34
B) $12378
C)
D) $5132

Answer 3

as I said, revenue = price * quantity = 515q = 515*34 = 17,510