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A farmer has 800 m of fencing and wishes to enclose a rectangular field. One side of the field is against a country road, which is already fenced, so the farmer needs to fence only the remaining three sides of the rectangular field. The farmer wishes to enclose the maximum possible area and wishes to use all of the fencings What dimensions of the fence would allow him to do this? Lesson 2.7 will teach you how to solve this kind of optimization problem. We will practice a few helpful skills first. (Note that this question has several parts). A diagram that represents the situation is given below, where the two parallel sides of the fence are denoted w (for width), and let the remaining side be denoted & (for length). Road Note that the area of the field can be expressed as A = ( x w. To maximize the the area of the field given the available fencing, we want to maximize A. To rewrite A = & x w into a function dependent on only one variable, consider the perimeter of the fence. Because the farmer wishes to use all 800 m of fencing, w and I will satisfy (choose all the correct choices) 0 2w + 1 = 800 0 1= 800 - 2w O w = 800 - 21 O w + 21 = 800