MAT137Y1 Midterm: MAT 137Y, 2007–2008Winter Session, Self Generated Solutions to Term Test 2.pdf

• School: UTSG
• Department: Mathematics
• Course: MAT137Y1
• Professor: all

Document Summary

Mat 137y, 2007 2008 winter session solutions to term test 2 (15%) 1. A farmer with 1500 feet of fencing wants to enclose a rectangular area and then divide it into four pens (fenced enclosures) with fencing parallel to one side of the rectangle. Find the largest possible total area of the four pens; be sure to verify that the area is indeed maximized. Let x be the length of the side of the eld with the ve parallel fences. The amount of fencing used is therefore 5x + 2y = 1500. We are asked to maximize the rectangular area, that is, 2x), where x must be between 0 and 300. A(x) = 750x 5 x2 = a(cid:48)(x) = 750 5x = 0 = x = 150. At the endpoints, a = 0, so the critical point must yield the maximum area, hence the largest possible area is 150 375 = 56250 square feet.