Question

Please help me when this question it would mean a lot I’m alll most out of time

Answer 1

The motel revenue based on the number of rooms rented and group rental are as follows;

(a) The price for renting three rooms is $195

(b) The formula through which the unit rate of a room is found is aₙ = 71 - 3·(n -1)

(c) The function for the revenue, R(n) = 74·n - 3·n²

(d) The most amount that can be made is $456

The number of rooms that gives the most amount is 12 rooms

What is a revenue in business?

A revenue is the total amount received for the sale of goods and services

The number of rooms in the motel = 44

The price for renting one room = $71

The price for renting two rooms = $68

The per room group rate = $71 - $3 for each additional room
(a) The amount made if a family rents three rooms is given as follows;

The unit price for two rooms = $71 - $3 = $68

The unit price for three rooms = $68 - $3 = $65

The price for the three rooms is therefore;

$65 × 3 = $195

(b) The formula that gives the rate charged for each room to an organization is an arithmetic progression, which can be expressed as follows;

aₙ = a₁ + (n - 1)·d

Where;

n = The number of rooms the organization plans to rent

a₁ = The first term of the arithmetic progression = 71

d = The common difference = -3

Which gives;

aₙ = 71 - 3·(n - 1)

The price for each room when an organization rents n rooms is therefore;

aₙ = 71 - 3·(n - 1)

(c) The revenue for renting n room is given by the formula;

Revenue, R(n) = Unit rate × Number of rooms

∴ R(n) = (71 - 3·(n - 1)) × n = 74·n - 3·n²

(d) The -ve coefficient of n² in the formula with which the revenue can be found indicates that the function has a maximum value. The number of rooms that gives the most revenue is obtained at the from the derivative of the R(n) as follows;

R'(n) = 74 - 6·n = 0

n = 74/6 ≈ 12

Which gives;

$R_{max}$ = R(12) = 74 × 12 - 3 × 12² = 456

The maximum revenue from renting to a single group ≈ $456

The number of rooms to rent that gives the maximum revenue is n ≈ 12

Learn more about the maximum value of a function here:

brainly.com/question/3028708

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