The cost C (in dollars) of producing x units of a product is C = 1

Part A

We divide the total cost by the number of units produced to get the average cost:

¯C(x)=1.15x+6000x=1.15+6000xC¯(x)=1.15x+6000x=1.15+6000x

Part B

When we produce x=600x=600 units, our average cost per unit is

C(600)=1.15+6000600=$11.15C(600)=1.15+6000600=$11.15

Part C

The long term behavior of the function is

limx→∞¯C(x)=limx→∞1.15+6000600=$1.15limx→∞C¯(x)=limx→∞1.15+6000600=$1.15

This essentially tells us the average cost of producing a limitless number of items, and tells us that no matter how many units we produce, the average cost will never get below $1.15 per unit.

Average Cost:

Cost is the amount of money spent to manufacture an xx amount of goods or services. The average cost, then, is the total cost divided by the number of good or services manufactured, i.e.

¯C(x)=C(x)xC¯(x)=C(x)x

Note that taking the limit of this function as xx grows without bound tells us the maximum cost we could possibly have (it essentially tells us the average cost of producing a limitless number of items).