Application of Max-Min Problems

1. A car rental agency rents 200 cars per day at a rate of $30 per day. For each $1

increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to

produce the maximum income? What is the maximum income?

2. A candy box is to be made out of a piece of cardboard that measures 8 by 12

inches. Squares of equal size will be cut out of each corner, and then the ends and

sides will be folded up to form a rectangular box. What size square should be cut

from each corner to obtain a maximum volume?

3. A family plans to fence in a rectangular patio area behind their house. They have

120 feet of fence to use. One side of the rectangle is the back of the house. What

should be the dimensions of the rectangular region if they want to make the patio

area enclosed as large as possible.

4. A manufacturer of storage bins plans to produce some open-top rectangular boxes

with square bases. The volume of each box is to be 125 cubic feet. material for

the base costs $6 per square foot, and material for the sides costs $3 per square

foot. Determine the dimensions of the box that will minimize the cost of materials.

5. The owner of a warehouse decides to fence in an area of 800 square feet behind

the warehouse. He plans to use the wall of the building as one of the four sides

that will enclose the rectangular area. He would like to use the least amount of

fencing necessary for the other three sides. How many feet of fence will be

needed.

Answers to Applications of Max-Min Problems

1. ; $35; $6125; x = 5

2. ; approx. 1.57 in

3. ; 30 X 60 = 1800

4. ; 5 X 5 X 5

5. ; 20 X 40