Orange-U-Happy is an orange-scented cleaning product that is manufactured in disposable cloth pads. Each box of 100 pads costs $5 to manufacture. The fixed costs for Orange-U-Happy are $40,000. The research development group of the company has determined the demand function to be q = -500p + 20,000, where p is the price for each box.
a. Write the expense equation in terms of the demand, q.
b. Express the expense function in terms of the price, p.
c. Determine a viewing window on a graphing calculator for the expense function. Justify your answer.
d. Draw and label the graph of the expense function.
e. Write the revenue function in terms of the price.
f. Graph the revenue function in a suitable viewing window. What price will yield the maximum revenue? What is the revenue at that price? Round answers to the nearest cent.
g. Graph the revenue and expense functions on the same coordinate plane. Identify the points of intersection using a graphing calculator, and name the breakeven points. Round to the nearest cent. Identify the price at the breakeven points.