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Suppose that c (x )equals 7 x cubed minus 70 x squared plus 13 comma 000 x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

User Aligator
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2 Answers

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Answer:

ummmm

Explanation:

idkk

User Aml
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6 votes

Answer:

A production level that will minimize the average cost of making x items is x=5.

Explanation:

Given that


c(x)=7x^3-70x^2+13,000x

is the cost of manufacturing x items

To find a production level that will minimize the average cost of making x items:

The average cost per item is
f(x)=(c(x))/(x)

Now we get
f(x)= 7x^2-70x+13000

f(x) is continuously differentiable for all x

Here x≥0 since it represents the number of items.,

Put x=0 in
7x^2-70x+13000

For x=0 the average cost becomes 13000


f(0)=7(0)^2-70(0)+13000


=13000

∴ f(0)=13000

To find Local extrema :

Differentiating f(x) with respect to x


f^(\prime) (x)=14x-70=0


14x=70


x=(70)/(14)

∴ x=5 gives the minimum average cost .

At x=5 the average cost is


f(5)=7(5)^2-70(5)+13000


=12825

∴ f(5)=12825 which is smaller than for x=0 is 13000

∴ f(x) is decreasing between 0 and 5 and it is increasing after 5.

User Jatobat
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