Question

The marginal cost of manufacturing x yards of a certain fabric is C'(x) = 3 − 0.01x + 0.000012x^2 (in dollars per yard). Find the increase in cost if the production level is raised from 2000 yards to 4000 yards.

Answer 1

$170,000

Explanation:

Integrating the marginal cost function gives us the cost function:

`C'(x) = 3-0.01x + 0.000012x^2\\\int\ {C'(x)} \, dx =C(x) = 3x-0.005x^2 + 0.000004x^3 +c`

The increase in cost from a raise in the production level, x, from 2000 yards to 4000 yards is given by:

`\Delta C = C(4000) - C(2000)\\\Delta C = 3*4000-0.005*(4000)^2 + 0.000004*(4000)^3 +c - (3*2000-0.005*(2000)^2 + 0.000004*(2000)^3 +c)\\\Delta C = \$170,000`

The increase in cost is $170,000.