Question

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?

Answer 1

If the pen has to be joined to the <i>whole</i> 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.

Answer 2

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.

Answer 3

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