1. Research has shown that for a company’s toy truck every increase of $0.10 in the price will result in 200 fewer sales. At one point, when the price was $2.35, the company sold 18,500 trucks. A reasonable employee of the company wondered aloud what price would maximize the revenue generated by the sale of the trucks for the company.
a) Determine the formula of the function N(x) that gives the number of trucks sold when the price is x dollars. Draw a graph of the function N(x).
b) Determine the formula for the function R(x) that gives the revenue generated when the price is x dollars. Graph y=R(x).
c) Determine algebraically the price that yields the maximum revenue. How much revenue is generated? How many trucks are sold at this price?
d) Let’s say that the company wants to sell 20,000 trucks. How much should they charge and how much revenue is generated?
e) What is the average rate of change in revenue from x=$2.50 to x=$2.85? What is the average rate of change from x=$3.00 to $3.25? What units are associated with the average rate of change? Interpret each average rate of change in the context of the given situation. What do these average rates of change tell you about the shape of the graph of R(x)?