Question

A farmer has 400 feet of fencing with which to build a rectangular pen. He will use part of an existing straight wall 100 feet long as part of one side of the perimeter of the pen. What is the maximum area that can be enclosed? Hint: Find an equation for the area of the pen using one variable then use your constraints to determine your interval values)

Answer 1

Sola to build fencing wall I ml reven- A farrer has 400ft of fencing to a rectangular pren. side of perimeter is 100 ft. long as encore from fig clearly seen 100th Primeter of Rectangular pen : = +100+*+/+* = 2y + &x+100=400 dy = 400-100-24 100+ of y = 150-2 We know Ачид ч Kachu palax Fun = xxx = 2 x (150-2) - 150 X-212 To Maxirize Area Take derivative and equate too. in A' (*) = 150-22=0 = 20 = 75 = 150-3 - 75 8. Maxium Area = axy = 75x75 A max = 5625) Ano