a farmer has 300 feet of fencing with which to enclose a rec

a farmer has 300 feet of fencing with which to enclose a rectangular grazing pen next to a barn. the farmer will use the barn as one side of the pen, and will use the fencing for the other three sides. find the dimensions of the pen with the maximum area

Solution

Only one side of is not being fenced.So if length =l and width =w

Length of fence = l +2w = 300

Area = l*w = (300 -2w)w

= -2w^2 + 300w

Max. Area is found at vertex x= -b/2a for ax^2 +bx +c

w = -(300)/(-2*2) = 75 feet

l= 300 -2*75 = 150 feet

Largest Area =75*150= 11250 ft^2