Question

It is known by Trade Kings that in the manufacturing of Chelsea Biscuits, fixed costs per month are K15,000. If the marginal cost is F(Q) = 0.000204Q² - 0.046Q + 6 when Q = 25 . Find the total cost function. 

Answer 1

Given

$$dC/dQ=F(Q)=0.000204Q^2-0.046Q+6$$

Then

$$C=\int(0.000204Q^2-0.046Q+6)dQ$$

$$=0.000068Q^3-0.023Q^2+6Q+K$$

Given $K=15000$ Therefore

$$C(Q)=0.000068Q^3-0.023Q^2+6Q+15000$$

If $Q=25$

$$C(25)=0.000068(25)^3-0.023(25)^2+6(25)+15000$$

$$=15136.69$$