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) = 95x + 23
(a) find the average cost function c.
c(x) = 1

(b) find the marginal average cost function c '.
c '(x) =2

(c) what happens to c(x) when x is very large?
lim_(x-> infinity) c(x) = 3

(a) The average cost function is

(b) The marginal average cost function is

(c) The average cost approaches to 95 if the production level is very high.

Step-by-step explanation:

(a) Suppose is a total cost function. Then the average cost function, denoted by , is

We know that the total cost for making x units of their Senior Executive model is given by the function

The average cost function is

(b) The derivative of the average cost function, called the marginal average cost function, measures the rate of change of the average cost function with respect to the number of units produced.

The marginal average cost function is

(c) The average cost approaches to 95 if the production level is very high.

(3x-8) or (3x+8)

step-by-step explanation:

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours