Question

You own a company with multiple lines of businesses. One of them is a plastic production plant that manufactures plastic parts for computer manufacturers as well as other businesses. When producing fewer than or equal to 20 units per week, the total cost function of the plant is described as TC(Q)=Q2+Q+10. If it were to produce more than 20 (per week), a second facility will be activated, changing the total cost function to TC(Q)=2Q+400. What is the average cost of making (the first) 10 units?

Answer 1

If fewer than or equal to 20 units are produced, then TC(Q) = Q^2 + Q + 10
If more than 20 units are produced, then TC(Q) = 2Q + 400

Total cost for 10 units is:

TC(10) = (10)^2 + 10 + 10
TC(10) = 100 + 10 + 10
TC(10) = 120

Average cost for 10 units is:

AC(10) = TC(10) / 10
AC(10) = 120 / 10
AC(10) = 12

So, average cost of making 10 units is 12