A rectangular field is to be fenced, one side of which is the edge of a straight river. It is given that the material for the two opposite side costs Php 3.00 per meter and the material for the side opposite the river costs Php 6.00 per meter. If an amount of Php 600.00 is available, what should be the dimensions to enclose the maximum area?

Answer 1

If the side parallel to the river has length x, and the other two sides have length y, we know that the cost is

6x+3*2y = 600
x+y=100

the area is

a = xy
= x(100-x)
That has a maximum at x=50.
So, the area is 50 by 50