§9.9 Homework
Math 1100-006
Solution Key
1. (4 points) (Problem 18a) Suppose that the total cost function for a commodity is C(x) =
1 2
300 + 6x + 20
x dollars. Find the marginal cost at x = 8 units and tell what this predicts
about the cost of producing 1 additional unit.
Solution: First, find the marginal cost function by differentiating:
M C = C 0 (x) = 6 +
1
x
10
The marginal cost at 8 units is
C 0 (8) = 6 +
8
= 6.8
10
This predicts that the additional cost to produce the 9th unit is approximately $6.80.
2. (Problem 24) The graph of a company’s total cost function is shown. For each problem,
use the graph to answer the following questions:
(a) (3 points) Will the 101st item or the 501st item cost more to produce? Explain.
(b) (3 points) Does this total cost function represent a manufacturing process that is
getting more efficient or less efficient? Explain.
Solution:
(a) You can see by drawing tangent lines that the slope of the tangent line is greater
at x = 500 than at x = 100, so the marginal cost is greater when x = 500. This
means that the 501st item costs more to produce than the 101st.
(b) The marginal cost is increasing, which means that the manufacturing process is
getting less efficient.