Sony Ent. is marketing a new smartphone. It determines that in order to sell x smartphones, the price per product must be p=280-0.4x. It also determine that the total cost of producing x smartphones is given by c(x)=5000+0.6x^2 .
a. Find the total revenue, R(x).
b. Find the total profit, P(x).
c. How many smartphones must the company sell in order to maximize profit?
d. What is the maximum profit?
e. What price per smartphone must be charged in order to maximize profit?
R(x) = x*p(x) = x(280-.4x)
P(x) = R(x)-C(x) = x(280-.4x) - (5000+.6x^2)
= -x^2 + 280x - 5000
dP/dx = -2x + 280
max profit at x = 140
now figure P(x) and p(x)