2 14 points TanApCalcBr10 34005 My Notes Ask Your Tea Custom

2. -14 points TanApCalcBr10 3.4.005. My Notes Ask Your Tea Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function, where C(x) is measured in dollars/year. C(x)-101x250000 (a) Find the average cost function C. C(x) - (b) Find the marginal average cost function c . (c) What happens to C(x) when x is very large? lim C(x) Interpret your results. O This value is what the production level approaches if the average cost per unit is very high O This value is what the average cost per unit approaches if the production level is very low O This value is what the average cost per unit approaches if the production level is very high O This value is what the production level approaches if the average cost per unit is very low

Solution

A) The average-cost function gives the average cost of making any number of desks. That would be the total cost of making the desks divided by the number of desks:

A(x) = (101x + 250,000)/x

B) The \"marginal\" cost is the cost of making one more desk. As you note, it is the first derivative of C(x), in this case 101.

C) If x is very large, they are making a sihtload of desks, and the 250,000 overhead pales to insignificance. The average cost approaches the marginal cost, 101.