The financial department in Example 3, using statistical and analytical techniques, arrived at the cost function

where C(x) is the cost (in millions of dollars) for manufacturing and selling x million cameras.

(A) Using the revenue function from Example 3 and the preceding cost function, write an equation for the profit function.

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

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

(D) Graph the profit function using an appropriate viewing window.

(E) Find the output to the nearest thousand cameras that will generate the maximum profit. What is the maximum profit to the nearest thousand dollars? Solve the problem graphically using the maximum command.

Data from Example 3

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:

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.

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.

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

Graph the revenue function using an appropriate viewing window.

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.

Transcribed Image Text:

C(x) = 156 + 19.7x Cost function