ECON 212, Spring 2018
Homework #16,
Due Thursday, April 5, in class
Assignment (all problems will be graded):
1. A company finds that if it produces x units of output, its costs will be
C(x) = 2x +9, and its revenue will be R(x) = -x² +12x
a) Find the output x that maximizes the firm's profits. Make sure to check the second order
condition.
b) Calculate the maximum profits.
c) For the company's break-even point(s).
d) Graph both the revenue and the cost functions on the same graph. Use graph paper.
Make sure to show the break-even points and the maximum profit point on the graph.
2. Suppose a bakery produces muffins. Let x be the bakery's output, boxes of muffins per day,
and y be average cost of production in $ per box. For the following average cost function, y =
6x² - 24x + 50,
a) Find the production level (boxes of muffins per day) at which the average cost is at a
minimum.
b) Show proof of the minimization by using the second derivative test.
c) Calculate the minimum average cost.
3. Repeat problem 2 the following average cost function, y = x² - 4x + 6.