Use -b/2a to determine the price that will yield the maximum profit. What is the maximum profit at that price?

Question

Review Questions:

use -b/2a to determine the price that will yield the maximum profit.

What is the maximum profit at that price?

What price will yield the maximum revenue?

What is the maximum revenue at that price?

What are the breakeven points for revenue equation?

What are the x-intercepts for revenue equation?

What are the breakeven points for profit equation?

What are the x-intercepts for profit equation?

Answer 1

Recap the original question:

E(p)=3.15(-112p+4500)+8000=-352.80p+22175.

R=pq=-112p²+4500p.

P=R-E=-112p²+4852.80p-22175. In this equation, a=112, b=4852.80.

For max P, -224p+4852.80=0, p=21.66=b/2a=4852.80/224.

Max P=-112(21.66)²+4852.80(21.66)-22175=30391.22, the maximum profit.

The breakeven point is when P=0 (R=E): -112p²+4500p=-352.80p+22175.

112p²-4852.80p+22175=0.

p=(4852.80±√4852.80²-4×22175×112)/224=38.1370 or 5.1916.

These are x-intercepts for the Profit Equation.

R=-112p²+4500p=p(-112p+4500)=8720.25 or 20343.50. These are the break even values for the revenue.