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Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is $C' (x) = 0.000009x^2 - 0.009x + 8$ where $C'(x)$ is measured in dollars/unit and $x$ denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $\$120$ . Find the total cost incurred by Lorimar in producing the first $500$ travel clocks/day.

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Volume of cubes and rectangular prisms: word problems

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Q. Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is

C' (x) = 0.000009x^2 - 0.009x + 8

where

C'(x)

is measured in dollars/unit and

x

denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is

\$120

. Find the total cost incurred by Lorimar in producing the first

500

travel clocks/day.

Calculate Marginal Cost: First, calculate the marginal cost for producing the first $500$ clocks using the marginal cost function $C'(x) = 0.000009x^2 - 0.009x + 8$ .
Plug $x = 500$ : Plug $x = 500$ into the marginal cost function: $C'(500) = 0.000009(500)^2 - 0.009(500) + 8$ .
Calculate $C'(500)$ : Calculate the value: $C'(500) = 0.000009(250000) - 0.009(500) + 8$ .
Simplify Calculation: Simplify the calculation: $C'(500) = 2.25 - 4.5 + 8$ .
Add Values: Add the values: $C'(500) = 2.25 - 4.5 + 8 = 5.75$ .

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