(1 point)
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 to 7500 yards.
Increase in cost $=\$ \square$
(Round to three decimal places as needed.)
Answer
Final Answer: The increase in cost is \(\boxed{585000.000}\)
Step 1 ：Define the marginal cost function as \(C^{\prime}(x)=3-0.01 x+0.000006 x^{2}\) (in dollars per yard).
Step 2 ：Calculate the increase in cost if the production level is raised from 1500 to 7500 yards. This is done by integrating the marginal cost function from 1500 to 7500.
Step 3 ：The result of the integration is 585000.000.
Step 4 ：So, the increase in cost when the production level is raised from 1500 to 7500 yards is \$585000.000.
Step 5 ：Final Answer: The increase in cost is \(\boxed{585000.000}\)
