Completing the Square Application Problems - Revenue

[Pages:3]Completing the Square Application Problems - Revenue

Important Definitions:

Revenue = (# items sold) x (Selling Price) Profit = (Revenue) - (Cost)

Lesson A: Revenue Problems

Example 1. A ferry operator takes tourists to an island. The operator carries an average of 500 people per day for $20 per person. The operator estimates that for each $1 increase in fare, 20 fewer people will take the trip. Let x be the number of $1 price increases. Create an equation to model the total revenue.

Example 2. Alex runs a snowboard rental business that charges $12.00 per snowboard and averages 36 rentals per day. She discovers that for each $0.50 decrease in price, her business rents out an additional two snowboards per day. At what price can Alex maximize her revenue?

Example 3. Tickets to a school dance cost $4.00 and the projected attendance is 300 people. For every $0.10 increase in ticket price, the dance committee projects that the attendance will decrease by 5. What ticket price will generate $1237.50 in revenue?

Example 4. A computer company selling game consoles sells 100 consoles in the average week at a price of $200 each. They find that for every $10 price decrease, 5 more consoles would be sold. If each console costs $50 to make, what should the selling price be in order to maximize profit?

MINIMUM/MAXIMUM WORD PROBLEMS ? REVENUE PROBLEMS

1. A theatre seats 2000 people and charges $10 for a ticket. At this price, all tickets can be sold. A survey indicates that if the ticket price is increased, the number sold will decrease by 100 for every dollar of increase. What ticket price would result in the greatest revenue? ($15.00)

2. If 400 people will attend a movie theatre when the admission price is $3.00 and if for every $0.10 increase in price, 10 fewer people attend, what price would yield the greatest gross receipts? ($3.50)

3. If 400 people will purchase a pen which cost $0.80 and 40 less people will buy the pen for every $0.10 increase in price, what price will yield the greatest sales? ($0.90)

4. A large car dealership has been selling new cars at $600 over the factory price. Sales have been averaging 80 cars per month. Due to inflation the $600 markup is going to be increased. The marketing manager has determined that for every $10 increase there will be one less car sold each month. What should the new markup be in order to maximize income?

5. A glassworks that makes lead-crystal bowls has a daily production cost C in dollars given by relation C = 0.2b2 ? 10b + 650, where b is the number of bowls made. How many bowls should be made to minimize the production cost? What is the cost when this many bowls are made? (25, $525)

6. Denise is an artist who works at a shopping center drawing "pencil portraits." She charges $20 per portrait and she has been averaging 30 portraits per week. She decides to increase the price, but realizes that for every one dollar increase she will lose one sale per week. If materials cost her $10 per portrait, what should she set the price at in order to maximize her profit? (Profit = Revenue ? Cost)

7. The TruTime Watch Company has been selling 1200 watches per week at $18 each. They are planning a price increase. A survey indicates that for every dollar increase in price there will be a drop of 40 sales per week. If it costs $10 to make each watch, what should the selling price be in order to maximize profit?

HW: Textbook pg. 313 # 17, pg. 317 # 14, pg. 281 # 19, 20

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