The local Employment Council would like to hold a charity event to raise money for the area Food Bank. They want to spend as little money as possible to rent a room and provide light refreshments. Everyone in attendance will pay an admission fee that will cover costs and include a profit. Any profit made will be donated to the local food bank. In order to minimize costs, they have quotes from three venues for the cost of an event of up to 80 people.

Question

The local Employment Council would like to hold a charity event to raise money for the area Food Bank. They want to spend as little money as possible to rent a room and provide light refreshments. Everyone in attendance will pay an admission fee that will cover costs and include a profit. Any profit made will be donated to the local food bank. In order to minimize costs, they have quotes from three venues for the cost of an event of up to 80 people.

Analyse the three quotes and answer the question below.

Where should the Employment Council have the event?

Venue 1
The Admiral Inn is offering a special rate of $17.99 per person and a minimum total charge of $400.00 to hold the event.

Venue 2
The Edward Country Club is offering a flat fee of $90.45 plus $14.99 per guest.

Venue 3
The Holiday Hotel is charging $500 for the first 25 guests and then $12.50 per guest after 25 guests are reached.

Answer 1

let the number of people be n

Venue1 = 17.99n + 400
Venue2 = 90.45 + 14.99n
venue3 = 500 + 12.5(n-25) , n ≥ 25

e.g. , suppose all 80 show up
venue1 = appr 1840
venue2 = appr 1290.45 ***
venue3 = 11845 , clearly way too much

at 25 guests
venue1 = 850
venue2 = 465.45 ***
venue3 = 500

at 20 guests
venue1 = 760
venue2 = 390.45 ***
venue3 = 500
clearly venue3 is the most expensive

are venue1 and venue2 ever the same?

17.99n + 400 = 90.45 + 14.99n
or more realistically
18n + 400 = 90.45 + 15n
3n = a negative

NO, venue 2 is always cheaper.

OK, I analysed it, but it should have been obvious from the beginning that venue2 would be the choice.

Answer 2

I asked my brother and he did not help me. Anyway, thank you

Answer 3

To analyze the three quotes and determine where the Employment Council should have the event, we need to calculate the total cost for each venue based on the number of guests (up to 80 people) and the pricing structure provided.

Venue 1:
The Admiral Inn has a special rate of $17.99 per person. However, they also have a minimum total charge of $400. For up to 80 people, the total cost can be calculated as follows:
Cost per person: $17.99 x 80 = $1,439.20
As this exceeds the minimum total charge of $400, the total cost for Venue 1 will be $1,439.20.

Venue 2:
The Edward Country Club has a flat fee of $90.45 plus $14.99 per guest. For up to 80 people, the total cost can be calculated as follows:
Flat fee: $90.45
Cost per guest: $14.99 x 80 = $1,199.20
Total cost for Venue 2: $90.45 + $1,199.20 = $1,289.65

Venue 3:
The Holiday Hotel is charging $500 for the first 25 guests and then $12.50 per guest after 25 guests are reached. For up to 80 people, the total cost can be calculated as follows:
Cost for the first 25 guests: $500
Remaining guests (80 - 25) = 55 guests
Cost per guest: $12.50 x 55 = $687.50
Total cost for Venue 3: $500 + $687.50 = $1,187.50

Based on the calculations, the Employment Council should choose Venue 3 - The Holiday Hotel. It offers the lowest total cost of $1,187.50 for up to 80 people, helping the council to minimize expenses and maximize the potential profit to be donated to the local food bank.