Answer to Question #212563 in Calculus for Akhona Klanisi

Question

Question  9

The marginal cost function for a good is given by

MC = −Q² + 80Q.

Find the total cost function if fixed costs are   500.

1. -^Q3/₃ +40 + 50
2. ^Q3/₃ +40Q² + C
3. -^Q3/₃ +80Q² + C
4. Q³ +80Q² + 500

Answer 1

$MC = -Q^2+80Q\\ \int MC dQ = \int (-Q^2 +80Q)dQ = -\cfrac{Q^3}{3}+40Q^2+C$

So total cost function if cost are 500 is:

$TC = -\cfrac{Q^3}{3}+40Q^2+500$