Answered

Find the best solutions to your problems with the help of IDNLearn.com's expert users. Our Q&A platform offers detailed and trustworthy answers to ensure you have the information you need.

A vendor sells pretzels on a city street corner.

He models the monthly costs, in dollars, to operate his business with the function [tex]C(x)[/tex], where [tex]x[/tex] is the number of pretzels he sells:

[tex]\[ C(x) = 0.63x + 800 \][/tex]

Because the vendor sells the pretzels for [tex]\$2.75[/tex] each, he models his monthly revenue from selling [tex]x[/tex] pretzels with the function [tex]R(x)[/tex]:

[tex]\[ R(x) = 2.75x \][/tex]

The function [tex]P(x)[/tex] represents the vendor's monthly profit, in dollars, when selling [tex]x[/tex] pretzels.

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

In a month where he sells 600 pretzels, the vendor will make a profit of [tex]P(600)[/tex] dollars. Calculate this profit.

Sagot :

GinnyAnsweridn
To determine the vendor's monthly profit when selling 600 pretzels, let's break down the problem step by step.

1. Calculate the Total Cost (C(x)) for 600 pretzels:
The cost function is given by:
[tex]\[ C(x) = 0.63x + 800 \][/tex]
Substituting [tex]\(x = 600\)[/tex]:
[tex]\[ C(600) = 0.63(600) + 800 = 378 + 800 = 1178 \][/tex]
So, the total cost for 600 pretzels is [tex]$1178. 2. Calculate the Total Revenue (R(x)) for 600 pretzels: The revenue function is given by: \[ R(x) = 2.75x \] Substituting \(x = 600\): \[ R(600) = 2.75(600) = 1650 \] So, the total revenue from selling 600 pretzels is $[/tex]1650.

3. Calculate the Profit (P(x)) for 600 pretzels:
Profit is given by the difference between revenue and cost:
[tex]\[ P(x) = R(x) - C(x) \][/tex]
Substituting the values for revenue [tex]\(R(600) = 1650\)[/tex] and cost [tex]\(C(600) = 1178\)[/tex]:
[tex]\[ P(600) = 1650 - 1178 = 472 \][/tex]

Therefore, when the vendor sells 600 pretzels in a month, he makes a profit of $472.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.