what is the dimensions of least amount of fencing contain 288,800 square meters

Question

a dairy farmer plans to enclose a rectangular pasture adjacent to a river.  To provide enough grass for the herd, the pasturs must contain 288,800 square meters. no fencing is required along the river. what dimensions will use the least amount of fencing?

 

solving optimization problems

Answer 1

Dimensions of rectangular enclosure are x and y so xy=288800m².

Length of fencing L=x+2y=x+577600/x.

dL/dx=1-577600/x²,

dL/dx=(x²-577600)/x²=(x-760)(x+760)/x²=0 at extrema, so x=760m (x has to be positive).

Therefore y=288800/760=380m and L=760+760=1520m.