The cost per unit in the production of an MP3 player is $60. The manufacturer charges $90 per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by $0.15 per MP3 player for each unit ordered in excess of 100 (for example, the charge is reduced to $87 per MP3 player for an order size of 120).
a.) The table shows the profits P (in dollars) for various numbers of units ordered, x. Use the table to estimate the maximum profit.
Units, x: 130, 140, 150, 160, 170
Profit, P: 3315, 3360, 3375, 3360, 3315
b.) Plot the points (x, P) from the table in part a. Does the relation defined by the ordered pairs represent P as a function of x? If it does, write the function and determine its domain. (Note: P = R - C, where R is revenue and C is cost.)