**Q: Suppose the marginal cost is: MC = 12 + 8x with C(10) = 1020. Find the fixed and total cost of producing 80 units.**

Answer:

We gotta know that the marginal cost is derivative of the cost. So, to find the cost function, we need to integrate the marginal cost function:

int[12 + 8x] = 12x + 4x^{2} + C

So, the cost function, C(x) = 12x + 4x^{2} + C

And we know that C(10) = 1020. So, we can plug in these values to solve for the constant C like so:

1020 = 12(10) + 4(10)^{2} + C

1020 = 120 + 400 + C

1020 = 520 + C

500 = C

So, the cost equation is:

C(x) = 12x + 4x^{2} + 500

The “C” value represents the “fixed costs”. So, the fixed costs are $500.

The total cost of producing 80 units can be found by calculating C(80):

C(80) = 12(80)+4(80)^2+500 = $27060

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thank you so much man, this example has helped me tons!!!!!!

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This was very helpful, thank you

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