A model for a​ company's revenue from selling a software package is ​R(p)=-2.5p^2+600p, where p is the price in dollars of the software. What price will maximize​ revenue? Find the maximum revenue.

Question

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Answer 1

R(p) =- 2.5p^2+600p

take the derivative and set equal to zero, and then solve for p

R'(p) = -5p + 600 = 0

5p = 600

p =600/5 = $120 = revenue maximizing price

plug that price into the revenue function to solve for maximum revenue

R(120) =-2.5(120)^2+ 600(120) = [600-2.5(120)](120) = 300(120) = $36,000 = maximum revenue