Question

using the cost function C(q) = q3−60q2+1200q+760 for 0 ≤ q ≤ 50 and a price per unit of $551.

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) = 551q

profit is revenue minus cost, so

P(q) = 551q - (q^3-60q^2+1200q+760)

You should probably graph P(q) to find the max. Take a look here:

http://www.wolframalpha.com/input/?i=551q+-+%28q^3-60q^2%2B1200q%2B760%29

If you have calculus as a tool, just find where dP/dq=0