Question

The revenue and cost functions for a particular product are given below. The cost and revenue are given in dollars, and x represents the number of units

R(x)=-0.8x²+608x

C(x)=256x+36720

(a) How many items must be sold to maximize the revenue?

(b) What is the maximum revenue?

(c) Find the profit function.

(d) How many items must be sold to maximize the profit?

(e) What is the maximum profit?

(f) At what production level(s) will the company break even on this product?

Answer 1

1.
R=-0.8x^2+608x
dR/dx=-1.6x+608
Maximizing occurs at dR/dx=0
=>x=608/1.6
=380

2.
=-0.8*380^2+608*380
=115520.00

3.
P=R-C=-0.8x^2+608x-256x-36720
=-0.8x^2+352x-36720

4.
dP/dx=-1.6x+352
Maximizing occurs at dP/dx=0
=>x=352/1.6
=220

5.
=-0.8*220^2+352*220-36720
=2000

6.
-0.8x^2+352x-36720=0
=>x=170,270