Question

Assume TC = 392 + 35Q + 2Q² . At what Q is average cost at its minimum?

Answer 1

Given,

To find the quantity at which our average cost will be minimum, we will first find the average cost by dividing the total cost by Q and then we will differentiate it:

Now, we will differentiate the above equation and keep it equal to 0 to find Q,

Now, to find whether our average cost is minimum or not we will do the second derivative test,

According to the second derivative test, the value of the function is minimum when the value of the second derivative test is greater than 0. So, from the above result, we can conclude that at Quantity 14 average cost is minimum.