Question

The function gives the cost to manufacture xitems.C(x) = 10,000 + 90x + 1200/x ; x=100Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where xis as indicated and h = 10 and 1.

(Use smaller values of h to check your estimates.)

(Round your answers to two decimal places.)

Answer 1

89.89 and 89.88

Explanation:

Given function,

`C(x) = 10000 + 90x + (1200)/(x)`

Where,

x = number of units manufactured,

Here, x = 100,

if h more items are produced then new number of units = 100 + h,

i.e. number of units ∈ [ 100, 100 + h]

If h = 10,

The number of units ∈ [100, 110],

Then the average cost per unit of manufacturing,

`=(C(110) - C(100))/(110 - 100)`

`=(10000 + 90(110) + (1200)/(110)-10000 - 90(100) - (1200)/(100))/(10)`

`=(900 + (1200(100 - 110))/(11000))/(10)`

`=(900-(12000)/(11000))/(10)`

`=(9900000 - 12000)/(110000)`

`=(9888000)/(110000)`

≈ 89.89

If h = 1,

The number of units ∈ [100, 101],

Then the average cost per unit of manufacturing,

`=(C(101) - C(100))/(101 - 100)`

`=(10000 + 90(101) + (1200)/(101)-10000 - 90(100) - (1200)/(100))/(1)`

`=90 + (1200(100 - 101))/(11000)`

`=90-(1200)/(11000)`

≈ 89.88