题目

Max与Min问题,
Suppose you have to use exactly 200 m of fencing to make ether one square enclosure or two separate square enclosures of any sizes you wish.what plan gives you the least area?the greatest area?要详解,

提问时间：2021-01-03

答案

Assume the side lengths of the two squares are a and b(when a or b equals 0, it is equivalent to making one enclosure). As the total length of the fencing is 200m, 4(a+b)=200, a+b=50->b=50-a.
The total area of the two squares will be a^2+b^2=a^2+(50-a)^2=2a^2-100a+2500=2(a-25)^2+1250
a has a value range of [0,50].
As a=25, b=25, it gives the min area 1250. The plan is to make two squares with side length of 25.
As a=50 or a=0, it gives the max area 2500. The plan is to make one square with side length of 50.