Suppose a small bicycle manufacturer makes cheap bikes that sell for 180$ each. The total cost of producing x bikes (in $) is given by c(x)=6000+240x-0.8x^2, where x is up to 200 bikes.
a. Write down the revenue function.
b. Graph the cost and revenue functions on suitable scales, for x from 0 to 200.
c. Find the break even point: the number of units (to the nearest whole number) which need to be produced for the revenue=cost. Use algebra.
d. Find the profit function p(x), and use this to find the number of units which produces the maximum profit. (hint: the marginal profit might help)
The solution shows how to find the cost, revenue, and profit functions for the bicycle manufacturer. It also shows how to find the break even point and maximize the profit.