Answer:
Option B- The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.
Step-by-step explanation:
Given :
The function [tex]c(x)=50+5x[/tex] represents price charged per customer where x is the number of $5 increases they charge over a rate of $50 per person.
The function [tex]p(x)=100-2x[/tex] represents the number of customers expected for the day, where x is the number of $5 increases they charge over a rate of $50 per person.
To find : (p⋅c)(2) mean about the horse-drawn carriage tour company.
Solution :
(p.c) means we multiply the p(x) and c(x)
[tex](p.c)(x)=p(x)\times c(x)[/tex]
[tex](p.c)(x)=(100-2x)(50+5x)[/tex]
[tex](p.c)(x)=5000+500x-100x-10x^2[/tex]
[tex](p.c)(x)=5000+400x-10x^2[/tex]
Substitute the value of x=2
[tex](p.c)(2)=5000+400(2)-10(2)^2[/tex]
[tex](p.c)(2)=5000+800-10(4)[/tex]
[tex](p.c)(2)=5800-40[/tex]
[tex](p.c)(2)=5760[/tex]
The horse-drawn carriage tour company can expect to take in $5760.
The function [tex]c(x)=50+5x[/tex] represents price charged per customer.
For x=2
[tex]c(x)=50+5(2)[/tex]
[tex]c(x)=50+10[/tex]
[tex]c(x)=60[/tex]
The charge per customer is $60.
Therefore, Option B is correct.
The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.
