MAX AND MIN PROBLEMS
MPM 2D1
Date:
Two numbers have a difference of 8. Find the numbers if their product is to be a minimum.
2. The sum of two 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. The sum of a number and three times another number is 18. Find the numbers if their product is a
maximum.
5. 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 to be a maximum. What is the maximum area?
6. A lifeguard marks off a rectangular swimming area at a beach with 200 m of rope. What is the
greatest area of water she can enclose?
7. A theatre seats 2000 people and charges $10 per ticket. At this price all the seats are sold. A survey
indicates that if the ticket price is increased, the number of tickets sold will decrease by 100 for every
dollar increase. V/hat ticket price will result in the greatest revenue? What is the greatest revenue?
8. A bus company carries about 20 000 riders per day for a fare of 90 A survey indicates that if the
fare is decreased, the number if riders will increase by 2000 for every 5 of decrease. What ticket
price would result in the greatest revenue?
.
Q
9. A car rental agency has 200 cars. The owner finds that a price of $36 per day he can rent all the cars.
For each $2 increase in price, the demand is less and 5 fewer cars are rented. What price will
maximize the total revenue? What is the maximum revenue?
10. A local cattle farmer has 1600 m of fencing to enclose and subdivide a rectangular field along a river
into 3 pens as shown in the diagram. The pens do not have to be the same size. No fencing is required
along the river. Determine the greatest area that can be enclosed by the entire fencing. What are the
dimensions of the entire field of maximum area?
River
Answers
0
5. 15Dm by 30Dm, 45000m2 6. 5000
1. 4,—4 2.6,6 3.10,—ID 4. 9,3
7. 15, $22500 8. 700 9. $58, $8410 10. 200m by 80Dm, 160000m2
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