Question

Rope and wire are arranged in the shape of a rectangle. Two parallel sides of the rectangle are made from the rope which costs $2.00 per foot. The other two sides are made from the wire which costs $3.00 per foot. Find the dimensions of the rectangle enclosing the most area which costs $100.00.

Looking for: max area
area= w x r
100=3w + 2r
w=100/3 - 2/3r
a(r)= (100/3 - 2/3r)r
a`(r)=100/3 - 4/3r
r=25
100=3w + 2r or 100=3w + 2(25)
w=50/3