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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.)

Respuesta :

Answer:

89.89 and 89.88

Step-by-step explanation:

Given function,

[tex]C(x) = 10000 + 90x + \frac{1200}{x}[/tex]

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,

[tex]=\frac{C(110) - C(100)}{110 - 100}[/tex]

[tex]=\frac{10000 + 90(110) + \frac{1200}{110}-10000 - 90(100) - \frac{1200}{100}}{10}[/tex]

[tex]=\frac{900 + \frac{1200(100 - 110)}{11000}}{10}[/tex]

[tex]=\frac{900-\frac{12000}{11000}}{10}[/tex]

[tex]=\frac{9900000 - 12000}{110000}[/tex]

[tex]=\frac{9888000}{110000}[/tex]

≈ 89.89

If h = 1,

The number of units ∈ [100, 101],

Then the average cost per unit of manufacturing,

[tex]=\frac{C(101) - C(100)}{101 - 100}[/tex]

[tex]=\frac{10000 + 90(101) + \frac{1200}{101}-10000 - 90(100) - \frac{1200}{100}}{1}[/tex]

[tex]=90 + \frac{1200(100 - 101)}{11000}[/tex]

[tex]=90-\frac{1200}{11000}[/tex]

≈ 89.88

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