The marginal cost of manufacturing $x$ yards of a certain fabric is
$$C ^ { \prime } ( x ) = 3 - 0.01 x + 0.000006 x ^ { 2 }$$
in dollars per yard. Find the increase in cost if the production level is raised from 1500 yards to 5500 yards.
A) $\$ 188,000.00$
B) $\$ 198,000.00$
C) $\$ 178,000.00$
D) $\$ 218,000.00$
E) $\$ 208,000.00$

Question

Quizplus · Accepted Answer

To find the increase in cost, integrate the marginal cost function $C'(x)$ from 1500 to 5500. The integral of $C'(x) = 3 - 0.01x + 0.000006x^2$ gives the total cost increase. Calculating this integral results in an increase of $\$198,000.00$.

The Marginal Cost of Manufacturing xxx Yards of a Certain Fabric Is

The Marginal Cost of Manufacturing $x$ Yards of a Certain Fabric Is