The function gives the cost to manufacture x items: [tex]C(x) = 15,000 + 80x + \frac{900}{x}[/tex]. If [tex]x = 100[/tex], what values of [tex]h[/tex] should be checked to estimate the cost? (Round your answers to two decimal places.)

A) [tex]x = 50[/tex]
B) [tex]x = 75[/tex]
C) [tex]x = 125[/tex]
D) [tex]x = 150[/tex]

Question

07-01-2025
Mathematics

High School

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The function gives the cost to manufacture x items: [tex]C(x) = 15,000 + 80x + \frac{900}{x}[/tex]. If [tex]x = 100[/tex], what values of [tex]h[/tex] should be checked to estimate the cost? (Round your answers to two decimal places.)

A) [tex]x = 50[/tex]
B) [tex]x = 75[/tex]
C) [tex]x = 125[/tex]
D) [tex]x = 150[/tex]

Answer :

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hameedha102 hameedha102 · Answer 1 · 2023-11-18T17:27:09-05:00

Final answer:

To estimate the cost effectively for manufacturing items using the provided function, values of x closest to 100, specifically x = 75 and x = 125, should be checked as they provide a good approximation of the cost change around the specified value.

Explanation:

The question asks to estimate the cost to manufacture a certain number of items using the given function C(x) = 15,000 + 80x + (900)/x when x = 100. To estimate the cost effectively, it makes sense to select values of x (or h as referred in the prompt) close to 100, as they will provide a good approximation of the cost change around the given value. Among the provided options, x = 75 and x = 125 are closest to 100. Hence, these values should be checked to estimate the cost change most accurately. Calculations for these values would involve simply substituting them into the cost function C(x) and rounding the answers to two decimal places.

For example, to calculate the cost for 75 items, one would substitute x with 75 in the equation resulting in: C(75) = 15,000 + 80(75) + 900/75. Similarly, for 125 items, the cost would be calculated by substituting x with 125.