Maximum & Minimum – Day 4 – “Revenue”
Revenue is the income a company receives from the sale of items or tickets. We can use this formula to solve problems involving maximizing revenue:
Revenue = (cost of item/ticket)x(number sold)
NOTE: If the price goes UP, the number sold goes DOWN.
If the price goes DOWN, the number sold goes UP.
Example 12
A theatre seats 2000 people and charges $10 for a ticket. At this price, all of the 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?
Understand the problem:
Known:2000 tickets
$10 cost
Cost+$1 results in #sold-100 / Find:
The greatest revenue
NOTE: revenue = (cost of ticket)(# tickets sold)
Solution:
So…..to maximize the revenueThe cost of tickets = $10 + $5
= $15
The number of tickets sold =
= 2000-500
= 1500 tickets sold / Check:
maximum revenue = 22500
revenue = (cost of ticket)(# tickets sold)
= 15 X 1500
= 22500
Example 13
A bus company carries about 20 000 riders per day for a fare of 90¢. A survey indicates that if the fair is decreased, the number of riders will increase by 2000 for each 5¢ decrease. What ticket price would result in the greatest revenue?
Understand the problem:
Known:20000 tickets
90¢ cost
Cost-5¢ results in #sold+2000 / Find:
The greatest revenue
NOTE: revenue = (cost of ticket)(# tickets sold)
Solution:
So…..to maximize the revenueThe cost of tickets =
The number of tickets sold = / Check:
Example 14
The Environmental Club sells sweatshirts as a fundraisers. They sell 1200 shirts a year at $20 each. They are planning to increase the price. A survey indicates that, for every $2 increase in price, there will be a drop of 60 sales a year. What should the selling price be in order to maximize the revenue?
Assignment: complete the worksheet on revenue word problems.
MPM2D1 / Name: ______WORKSHEET – Maximum & Minimum Revenue Problems
1. Studies have shown that 500 people attend a high school basketball game when the admission price is $2.00. In the championship game admission prices will increase. For every 20¢ increase 20 fewer people will attend. What price will maximize receipts?
2. The Transit Commission’s single-fare price is 60¢ cash. On a typical day, approximately 240000 people take transit and pay the single-fare price. To reflect higher costs, single fare prices will be increased, but surveys have shown that every 5¢ increase in fare will reduce rider-ship by 5000 riders daily. What single-fare price will maximize income for the commission based on single fares?
3. Slacks incorporated sold 6000 pairs of slacks last month at an average price of $44 each. The store is going to increase prices in order to increase revenue. Sales forecasts indicated that sales will drop by 200 for every dollar increase in price. What price will maximize revenue?
4. An auto parts store currently sells 300 spark plug packages each week at a price of $6.40 each. To increase sales and reach more customers the parts outlet decides to reduce the price of the package, knowing that every $10 decrease in price will result in 5 more sales. What price will maximize total revenue?
5. Tri Electronics sells radios for $50 each. 40 radios are sold daily. a survey indicates that a price raise of $1 will cause the loss of one customer. How much should the company charge to maximize revenue?
6. A company selling cassette tape recorders for $80, sells 60 each day. A survey indicates that for each dollar the price is raised, one customer will be lost.
a. How much should the company charge to maximize the revenue?
b. The cost of making the recorders is $54 each. How much should the company charge to maximize profit?