This is a continuation of Example 7 in Section 2.1. Recall that the financial department in the

Question:

This is a continuation of Example 7 in Section 2.1. Recall that the financial department in the company that produces a digital camera arrived at the following price–demand function and the corresponding revenue function:

p(x) 94.8 5x R(x) = xp(x) = x(94.8 - 5x) = Price-demand function Revenue function

where p(x) is the wholesale price per camera at which x million cameras can be sold and R(x) is the corresponding revenue (in millions of dollars). Both functions have domain 1 ≤ x ≤ 15.

(A) Find the value of x to the nearest thousand cameras that will generate the maximum revenue. What is the maximum revenue to the nearest thousand dollars? Solve the problem algebraically by completing the square.

(B) What is the wholesale price per camera (to the nearest dollar) that generates the maximum revenue?

(D) Find the value of x to the nearest thousand cameras that will generate the maximum revenue. What is the maximum revenue to the nearest thousand dollars? Solve the problem graphically using the maximum command.

Data from Example 7

A manufacturer of a popular digital camera wholesales the camera to retail outlets throughout the United States. Using statistical methods, the financial department in the company produced the price–demand data in Table 4, where p is the wholesale price per camera at which x million cameras are sold. Notice that as the price goes down, the number sold goes up.

Table 4 Price-Demand x (millions) 2 in 00 5 8 12 p($) 87 68 53 37