## 20. BUSINESS The function f(x) = 1000-0.01x² models the manufacturing cost per item when x items are produced, and g(x) = 150-0.001x² m

Question

20. BUSINESS The function f(x) = 1000-0.01x² models the manufacturing cost per item when x items are produced,

and g(x) = 150-0.001x² models the service cost per item. Write a function C(x) for the total manufacturing and

service cost per item.

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2021-10-16T17:33:01+00:00
2021-10-16T17:33:01+00:00 1 Answer
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## Answers ( )

Answer:Profit is calculated by subtracting the total cost from the total revenue as expressed in the equation given above as,

P(x) = R(x) – C(x)

If we are to substitute the given expression for each of the terms, we have,

P(x) = x(S(x)) – C(x)

Substituting,

P(x) = x(30 – 0.01x) – (0.15x³ + 0.01x² + 2x + 120)

Simplifying,

P(x) = 30x – 0.01x² – 0.15x³ – 0.01x² – 2x – 120

Combining like terms,

P(x) = -0.15x³ – 0.02x² + 28x – 120

The answer to this item is the second among the choice, number 2.

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