1. Cost function. The management of a company that manufactures surfboards has fixed costs (at 0 output) of $200 a day and total costs of $3,800 per day at a daily output of 20 boards.
a. Assuming the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function.
b. What are the total costs for an output of 12 boards per day?
c. Graph the cost function for .
2. Price-demand function. A manufacturing company is interested in introducing a new power mower. Its market research department gave the management the price-demand forecast listed in the table below.
Demand x Wholesale Price p(x)
a. Plot these points, letting P(x) represent the price at which x number of mowers can be sold (demand). Label the horizontal axis x.
b. Note that the points in part a lie along a straight line. Find an equation for the price-demand function.
c. What would be the price for a demand of 3,000 units?
d. Write a brief verbal interpretation of the slope of the line found in part b.