10 Ex: Suppose you wish to fence in a rectangular shaped field on your farm. You have 3000 m of fencing to use. What dimensions of the field will give a maximum area? Ex: An open top box is made by cutting equal squares from each corner of a piece of cardboard measuring 10 inches by 15 inches and then folding up the resulting flaps. What are the dimensions that yield the largest volume, and what is that volume? Ex: A farmer wants to fence in a rectangular shaped pasture on his land. One side of the pasture will be along a river and will not need to be fenced. He has 500 yards of fencing material to use. What is the maximum area he can fence in?