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

The given cost function is:

c(x)=94x+270000c(x)=94x+270000

(a)

Finding the average cost function:

C(x)=94x+270000xC(x)=94+270000xC(x)=94x+270000xC(x)=94+270000x

(b)

Finding the marginal average cost function:

We have,

C(x)=94+270000xC(x)=94+270000x

Differentiating with respect to x we get,

C′(x)=−270000x2C′(x)=−270000x2

(c)

We have,

C(x)=94+270000xC(x)=94+270000x

Finding the average cost at x→∞x→∞:

limx→∞C(x)=limx→∞94+270000xlimx→∞C(x)=94+270000∞limx→∞C(x)=94+0limx→∞C(x)=94limx→∞C(x)=limx→∞94+270000xlimx→∞C(x)=94+270000∞limx→∞C(x)=94+0limx→∞C(x)=94

Implies that, as the number of units increases the average cost reaches to $94 per unit.