Mr. Farmer has a problem that he knows can be solved mathematically. He owns land and wants to fence in a rectangular portion for his horses. He has 200 feet of fence. He could guess at the measurements that would give his horses the largest grazing area but why should he guess when he has you to help him solve this problem with algebra.
1. Determine how he can maximize his area. Set up an equation that will maximize the area of the rectangular field
2. Graph the area function.
3. If Mr. Farmer wants to enclose the largest possible rectangular area,
a. What should the length of the field be?
b. What should the width of the field be?
c. What is the maximum area that these dimensions will yield?
4. What is the meaningful DOMAIN? Explain why you picked these values.
5. What is the meaningful RANGE? Explain why you picked these values.