q=-112p+4500 and E(q)=3.15q+8000

Question

Write the expense equation in terms of the price, p

Use R=pq to write the revenue equation in terms of the price.

Use P=R-E to write the profit equation in terms of the price

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

What is the maximum profit at that price?

Answer 1

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.