Part A

To get the average cost, we divide the total cost by the number of items sold, i.e.

¯C(x)=C(x)x=x2+38x+2300x=x+38+2300xC¯(x)=C(x)x=x2+38x+2300x=x+38+2300x

So if the company sold 467 computers, then the average cost per computer is

¯C(467)=467+38+2300467≈$509.93C¯(467)=467+38+2300467≈$509.93

Part B

To get the marginal average cost function, we differentiate the average cost:

¯C′(x)=ddx(x+38+2300x)=1−2300x2C¯′(x)=ddx(x+38+2300x)=1−2300x2

Average Cost:

Recall that in economics cost is a function that describes how much money it takes to manufacture xx items. To find the average cost then, we need to divide by the total number of items sold:

¯C(x)=C(x)xC¯(x)=C(x)x

Also, recall that the marginal average cost is the derivative of the average cost function.