Optimization Problem list for Exam 2 Winter '23:
1.
An animal shelter has 160 feet of fencing to enclose two adjacent rectangular playpen
areas for dogs.
What dimensions should be used so the the enclosed area will be a maximum?
2.
A storage box with a square base must have a volume of 80 cubic centimeters.
The top
and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter.
Find the dimensions that will minimize cost.
3.
A net enclosure for golf practice is open at one end (see 3.4 #14). The volume of the
enclosure is 83 1/3 cubic meters. Find the dimensions that require the least amount of netting.
4.
A strawberry farmer will receive $30 per bushel of strawberries during the first week of
harvesting.
Each week after that, the value will drop $0.80 per bushel.
The farmer estimates
that there are approximately 120 bushels of strawberries in the fields, and that the crop is
increasing at a rate of 4 bushels per week.
When should the farmer harvest the strawberries to
maximize their value?
How many bushels of strawberries will yield the maximum value? What
is the maximum value of the strawberries?
5.
A rectangular package to be sent by a postal service can have maximum combined
length and girth (perimeter of a cross section) or 108 inches. Find the dimensions of the
package with maximum volume. Assume the package's dimensions are x by x by y.
6.
Find the length and width of a rectangle that has perimeter 48 meters and maximum
area.
7.
When a wholesaler sold a product at $40 per unit, sales were 300 units per week. After a
price increase of $5, the number of units sold dropped to 275 units per week. Assuming the
demand function is linear, what price per unit will maximize the weekly revenue? (3.5 #21)
