To find the total increase in cost, we need to calculate the difference between the total cost of producing 200 units and the total cost of producing 100 units.
The total cost function (TC) is the integral of the marginal cost function (MC), so we can find the total cost of producing x units by integrating MC with respect to x:
TC = ∫ MC dx
Integrating MC, we get:
TC = 0.001x^3 + 0.3x^2 + 40x + C
where C is the constant of integration.
To find C, we need to know the total cost of producing some number of units. Let's assume that the total cost of producing 100 units is $5000:
5000 = 0.001(100)^3 + 0.3(100)^2 + 40(100) + C
Solving for C, we get:
C = 5000 - 100 + 0.03 + 40,000
C = 44,900
So the total cost function is:
TC = 0.001x^3 + 0.3x^2 + 40x + 44,900
Now we can calculate the total cost of producing 100 units and 200 units:
TC(100) = 0.001(100)^3 + 0.3(100)^2 + 40(100) + 44,900 = $50,900
TC(200) = 0.001(200)^3 + 0.3(200)^2 + 40(200) + 44,900 = $86,300
The total increase in cost is the difference between TC(200) and TC(100):
TC(200) - TC(100) = $86,300 - $50,900 = $35,400
Therefore, the total increase in cost is $35,400.