A fence is to be built to enclose a rectangular area of 240 square feet. Find the dimensions for the fence that is the most economical to construct.

Question

The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 15 dollars per foot.

Please help!!!

Answer 1

xy=240

C(ost)=3*3x + 15y = 9x+15*240/x

dC/dx=9-(15*240/x²)=0 at the minimum point

9x² = 15*240 => x=20 and y=12