side parallel to river --- y m
each of other two sides --- x
2x + y = 600 ---> y = 600-2x
area = xy
= x(600-2x) = -2x^2 + 600x
d(area)/dx = -4x + 600
= 0 for a max of area
-4x = -600
x = 150
then y = 600-2x = 300
largest area = 150(300) = 45000 m^2
You plan to enclosed part of a rectangular farmland with a fence. Since one side of it is bounded by a river, you only need to fence the other three sides. if you have enough budget to buy 600m of fencing material, what is the largest area you can enclose?
1 answer
1 answer