A rancher has 5 comma 7005,700 feet of fencing available to enclose a rectangular area bordering a river.

Question

A rancher has 5 comma 7005,700 feet of fencing available to enclose a rectangular area bordering a river. He wants to separate his cows and horses by dividing the enclosure into two equal areas. If no fencing is required along the river, find the length of the center partition that will yield the maximum area. what is the length of the center partition that will yield the maximum area?

Answer 1

Let x = length of side parallel to the river

     y = length of each of the other sides 

 

Then, x + 3y = 5,700

 

So, x = 5700 - 3y

 

Area = xy = (5700 - 3y)(y) = -3y² + 5700y, where 0 < y < 1900

 

The graph of the area function is part of a parabola which opens downward.  

 

Maximum area when y = -5700/[2(-3)] = -5700/(-6) = 950 ft