Quiz – sections 2



Maximum & Minimum – Day 1

Example 1

A ball thrown vertically is ‘h’ metres above the ground after ‘t’ seconds, where [pic]. What is the maximum height of the ball, and when does it reach that height?

Example 2

A ball thrown into the air from the balcony of an apartment building and falls to the ground. The height, h, in metres, of the ball relative to the ground, t, seconds after being thrown is given by [pic].

a. Find the maximum height of the ball above the ground.

b. How long does it take the ball to reach maximum height?

c. How high is the balcony above the ground?

d. After how many seconds does the ball hit the ground?

Example 3

A projectile is launched from a platform, and its height, h, in metres is given as a function of the elapsed time, t, in seconds by [pic].

a. What is the maximum height of the projectile?

b. How long does it take the projectile to reach its maximum height?

c. How long does it take the projectile to reach the ground?

Assignment: Section 6.1 Page 271 #12-15, 21

Mathpower 10: page 236 #14-17, 22

Maximum & Minimum – Day 2 – “Numbers”

Example 4

The sum of two numbers is 60. Find the numbers if their product is a maximum.

Example 5

The sum of two numbers is 28. Find the numbers if the sum of their squares is a minimum.

Example 6

Two numbers have a difference of 16. Find the numbers if the result of adding their sum and their product is a minimum.

Example 7

The sum of a number and three times another number is 18. Find the numbers if their product is a maximum.

Assignment:

1. Complete example 7 above.

2. The sum of two natural numbers is 12. If their product is a maximum, find the numbers.

3. Two numbers have a difference of 20. Find the numbers if the sum of their squares is a minimum.

4. Page 272 #18, 20, 22 (Day1 type questions) Mathpower 10: Page 235 #10, 11

Maximum & Minimum – Day 3 – “Area”

Example 8

A rectangular lot is bordered on one side by a stream and on the other three sides by 600 m of fencing. Find the dimensions of the lot if its area is a maximum.

Example 9

A lifeguard marks off a rectangular swimming area at a beach with 200 m of rope. What is the greatest area of water that she can enclose?

Example 10

What is the maximum area of a triangle having 16 cm as the sum of its base and height?

Example 11

A rectangular area is to be enclosed by a fence. Two fences, parallel to one side of the field, divide the field into 3 equal rectangular fields. If 2400 m of fencing is available, find the dimensions of the field giving the maximum area.

Assignment:

1. Page 237 # 19, 23, 24, 26 AND

2. A landscaper wishes to enclose a rectangular rest area with trees planted 1 m apart along the boundary. The perimeter of the area is to be 120 m. What will the maximum area of the rest area be?

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)

Remember: 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?

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?

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:

1. Page 272 #16 (see example 4 on page 269)

2. complete the worksheet on revenue word problems.

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?

-----------------------

Answers:

1. $3.50 2. $1.50 3. $37 4. $6.20

5. $45 6.a. $70 b. $97

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download