calculus problem...

Question

A manufacturer has a fixed cost of $85,000 and variable costs given by V(x)= 0.000004x^3-0.05x^2+410x, where x is the number of items produced. The manufacturer sells the items for $320 each. Find the total cost function C(x), the total revenue function R(x), and the total profit function P(x). The use P(x) to find the profit or loss when 2,000 items are produced and sold and when 5,000 items are produced and sold.

Answer 1

PROBLEM

A manufacturer has a fixed cost of $85,000 and variable costs given by V(x)= 0.000004x^3-0.05x^2+410x, where x is the number of items produced. The manufacturer sells the items for $320 each. Find the total cost function C(x), the total revenue function R(x), and the total profit function P(x). The use P(x) to find the profit or loss when 2,000 items are produced and sold and when 5,000 items are produced and sold.

SOLUTION

C(x) = 85000 + V(x)

R(x) = 320x

P(x) = R(x) - C(x)

Find P(2000) and P(5000) by substituting 2000 and 5000 into P(x) wherever x appears.