Calculus
posted by Jessica .
a farmer has 160 ft of fence and wants a pen to adjoin to the whole side of the 130 ft barn. what should the dimensions be for maximum area?

If the pen has to be joined to the whole side of the barn, there goes 130 ft. He/she has only 30 ft left for the two sides. The dimensions are therefore 15 ft * 130 ft = 1950 sq.ft.
There is no calculations involving calculus, unless I have misinterpreted the question. 
A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $30/ft and on the other three sides by a metal fence costing $20/ft. If the area of the garden is 108 square feet, find the dimensions of the garden that minimize the cost.

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $30/ft and on the other three sides by a metal fence costing $20/ft. If the area of the garden is 108 square feet, find the dimensions of the garden that minimize the cost.
Length of side with bricks x
Length of adjacent side y 
lol