Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Bea T. Howen, a sophomore college student, lost her scholarship after receiving a D in her "Music Appreciation" course. She decided to buy a snow plow to supplement her income during the winter months. It cost her $6312.50. Fuel and standard maintenance will cost her an additional $8.75 for each hour of use. Find the cost function C(x) associated with operating the snow plow for x hours. C(x)= If she charges $34.00 per hour write the revenue function R(x) for the amount of revenue gained from x hours of use. R(x)= Find the profit function P(x) for the amount of profit gained from x hours of use. P(x)= How many hours will she need to work to break even? hours

Sagot :

MrRoyal

Answer:

[tex](a)\ C(x) = 6312.50 + 8.75x[/tex]

[tex](b)\ R(x) = 34x[/tex]

[tex](c)\ P(x) = 6312.50 -25.25x[/tex]

[tex](d)\ Break\ Even = 250\ hours[/tex]

Step-by-step explanation:

Solving (a): The cost function.

Given

[tex]Cost = \$6312.50[/tex] --- cost of saxophone

[tex]Additional = \$8.75[/tex] per hour

The cost function is: sum of the cost of the saxophone and the extra cost per hour.

If an hour costs 8.75, then x hours will cost 8.75x

So, the cost function is:

[tex]C(x) = Cost + Additional[/tex]

[tex]C(x) = 6312.50 + 8.75x[/tex]

Solving (b): The revenue function

Given

[tex]Charges = \$34.00[/tex] per hour

The revenue function is the product of the unit charge by the number of hours.

If in an hour, she charges $34.00, then in x hours, she will cost 34x

So, the revenue function is:

[tex]R(x) = Charges * Hours[/tex]

[tex]R(x) = 34.00 * x[/tex]

[tex]R(x) = 34x[/tex]

Solving (c): The profit function

This is the difference between the cost function and the revenue function

i.e.

[tex]P(x) = C(x) - R(x)[/tex]

So, we have:

[tex]P(x) = 6312.50 + 8.75x - 34x[/tex]

[tex]P(x) = 6312.50 -25.25x[/tex]

Solving (d): The break even hours.

To do this, we simply equate the cost function and the revenue function, then solve for x

i.e.

[tex]C(x) =R(x)[/tex]

[tex]6312.50 + 8.75x = 34x[/tex]

Collect like terms

[tex]6312.50 =- 8.75x + 34x[/tex]

[tex]6312.50 = 25.25x[/tex]

Solve for x

[tex]x = \frac{6312.50}{25.25}[/tex]

[tex]x = 250[/tex]

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.