Question

a. A rectangular pea is built with one side against a bam. If 1200 m offencing are used for the other three sides of the pon, what dimensions made the area of the pen? b. A rancher plans to make four identical and adjacent rectangular pens against a bam, each with an area of 225 offence that mus be used segure) What are the dimensions of each pon that minimize the amount a. Let A be the area of the rectangular pen and it be the length of the sides perpendicular to the bar whethe tive function in a form that does not include the length of the side paralel to the bar A 1200x - 2x (lype an expression> The interval of interest of the objective function 1.600 (Simplify your answer Type your answe r val notation Do not use o n the individual endpoints) To maximize the area of the pen the sides perpendicular to the burn should be 300 m long and the side panel to the bam should be 600 m long Type exact answers using cals as need b. Lot be the length of the sides perpendicular to them and lot be the fallenge offence needed to the objective function LI ype an expression)

Answer 1

– Guvern length of fence on 3 sides is 1200 xt at l = 1200 2x + 1 = 1200 - 5 &= 1200-22 Area - A= length & breadth A= exa A = (1200-2x) a A = 1200x-2x. To maximize Area, put da = 0 da = (1200x -zx-) -0 1200 - 48=0 x=300. - - 1200 - 22= 1200 - 2(300) = 1200-600 l=600 Domensions for moimum are, d=600, x=300

10 Lite - - Area of Each Pen 225 ml length x breadth xxl. ex=225. 2) - 225 Total length of fence - 5x+4 e needed L= 5x+4l. = 5x + 4 (225) 12= 5x + 900 To minimise 'ť, put d o die (52+ 900) - 5-90030 su- 900 x- 1180 = 655 x 180 i l: 7.5 ls Domensions of each pes are 655 and 7.585 m.