How do I find the formulas and the max profit

Question

A travel agency offers a package for

​$2000

per person if they have

50

or less sign up. For each person in excess of

50​,

the agency reduces the price by

​$10

for every traveler.

​(a) Complete the table to explore the relationship between price and revenue numerically.

​(b) Generalize the numerical pattern in the table to write formulas for the price as a function of number of travelers and revenue as a function of travelers.

​(c) What number of travelers must sign up to produce the maximum​ revenue?

What is the maximum revenue and what will each passenger​ pay?

​(d) It will cost the travel agency

​C(n)=9000+400n

for this trip if they have n travelers.

Determine the number of travelers needed to produce the maximum profit.

What is the maximum profit and what will each passenger​ pay?

A travel agency offers a package for

​$2000

per person if they have

50

or less sign up. For each person in excess of

50​,

the agency reduces the price by

​$10

for every traveler.

​(a) Complete the table to explore the relationship between price and revenue numerically.

​(b) Generalize the numerical pattern in the table to write formulas for the price as a function of number of travelers and revenue as a function of travelers.

​(c) What number of travelers must sign up to produce the maximum​ revenue?

What is the maximum revenue and what will each passenger​ pay?

​(d) It will cost the travel agency

​C(n)=9000+400n

for this trip if they have n travelers.

Determine the number of travelers needed to produce the maximum profit.

What is the maximum profit and what will each passenger​ pay?

a) Complete the table.

Number of​ Travelers, n	Price per​ person, p(n)	Revenue​ R(n)
50	​$	​$
51	​$	​$
52	​$	​$
60	​$	​$

​(b) The table shows the revenue climbs if more than

50

travelers sign up for the package.

Write the formula for the price if n people sign up for the​ trip,

n≥50.

​p(n)=

Write the formula for the revenue from n​ travelers,

n≥50.

​R(n)=

Answer 1

p represents each additional person

R(p) = (2000 - 10p)(50 + p)