Question

1. The Gilbert Drama Guild is having a fund-raiser dinner at a local restaurant. While the food, beverages and live entertainment are all being donated by the restaurant, the guild is responsible for paying for decorations and the printing of tickets. The guild estimates that these expenses will total $500. A maximum of 200 tickets will be sold and each ticket will cost $40. Because all guild members are required to purchase a ticket to the fund-raiser, a minimum of 30 tickets will be sold.
The function that models the amount of money that the guild will raise with this fund-raiser is modeled by the function , where x is the number of tickets sold.
(a) What is the practical domain of the function in this situation?
(b) What is the practical range of the function in this situation?
Answer:

Answer 1

Total estimation of the expenses = $500.

Maximum number of tickets = 200 tickets.

Each ticket cost = $40.

Minimum number of tickets could be sold = 30 tickets.

x is the number of tickets sold.

f(x) is the total expenses of all tickets.

So, we can setup function as

f(x) = 40x.

We need to find the domain in first part.

Minimum number of tickets are 30.

Let us find maximum number of tickets for total expenses = $500.

40x = 500.

Dividing both sides by 40, we get

x= 12.5 approximately 13 tickets.

But we also given minimum number of tickets 30 and total number of tickets = 200.

So, domain would be integers from from 30 to 200. that is [30,200].

And let us find total amount for minimum 30 tickets would be = 30*40 = $1200.

And total amount for maximum  tickets would be = 200 * 40 = $8000.

So, the range would be integers from $1200 to $8000 that is [1200,8000].