Break-even analysis: The following table contains price-demand and total cost data for the production of treadmills, where p is the wholesale price (in dollars) of a treadmill for an annual demand of x treadmills and C is the total cost (in dollars) of producing x treadmills.
x p ($) C ($)
2,910 1,435 3,650,000
3,415 1,280 3,870,000
4,645 1,125 4,190,000
5,330 910 4,380,000
a. Find a linear regression equation for the price-demand data, using x as the independent variable.
b. Find a linear regression equation for the cost data, using x as the independent variable. Use this equation to estimate the fixed costs and the variable costs per treadmill.
c. Graph the cost function and the revenue function in same diagram.
d. Find the break-even points.
e. Find the price range for which the company will make a profit.