Question

Jack has 800 feet of fencing to fence off a rectangular field that borders a straight river. HE DOESN'T NEED TO FENCE ALONG THE RIVER. What are the dimensions( L and W ) of the field that has the largest area? What is the largest area?

Answer 1

2W+L=800andwe want to maxmize the areaarea=WLL=800-2Wso area=W(800-2W)=800W-2W^2area'=800-4Wto find critcal numbers set area'=0800-4W=04W=800W=200andL-800-2(200)=400so maximum area is 400(200)=80000