2. MAT 150 Module 8 – Rational Functions Lesson 2 – Rational Equations and Applications https://sites.google.com/site/conicsectionshyperbolas/_/rsrc/1433254688151/home/real- life-example-2/Hyperbola%20Smokestack.png?height=188&width=303

3. Applications of Rational Functions In this lesson we will look at an application of rational functions and equations – the average cost functions. The average cost is called It is defined as Cost/Number of Items or

4. Application Financial analysts in a company that manufactures ovens arrived at the following daily cost equation for manufacturing x ovens per day: C(x) = x 2 + 4x + 1800. a.Find the rational function.

5. Solution – Part a

6. Application Financial analysts in a company that manufactures ovens arrived at the following daily cost equation for manufacturing x ovens per day: C(x) = x 2 + 4x + 1800. b. What is the average cost when 100 ovens are produced per day?

7. Solution – Part b

8. Application Financial analysts in a company that manufactures ovens arrived at the following daily cost equation for manufacturing x ovens per day: C(x) = x 2 + 4x + 1800. c. If the average cost is $139 per oven, how many ovens were produced per day?

9. Solution – Part c c. If the average cost is $139 per oven, how many ovens were produced? Set = 139 and solve for x. 139 = We can use the graphing calculator to solve.

10. Solution – Part c

11. Application Financial analysts in a company that manufactures ovens arrived at the following daily cost equation for manufacturing x ovens per day: C(x) = x 2 + 4x + 1800. d. For what daily production level (to the nearest integer) is the average cost per unit at a minimum, and what is the minimum average cost per oven (to the nearest cent)?

12. Solution – Part d We can also find the minimum point from the graph. Remember that x represents the minimum number of ovens and y represents the minimum average cost. So 42 ovens should be produced for a minimum average cost of $88.85 per oven.