# SOLUTION: A rectangular field having an area of 2700 m^2 is to be enclosed by a fence, and an additional fence is to be used to divide the field in the middle. The cost of the fence down the

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 Question 453862: A rectangular field having an area of 2700 m^2 is to be enclosed by a fence, and an additional fence is to be used to divide the field in the middle. The cost of the fence down the middle is \$24 per running meter, and the fence along the sides cost \$36 per running meter. Estimate the dimensions of the field so that the total cost of the fencing material is least. Answer by ankor@dixie-net.com(15660)   (Show Source): You can put this solution on YOUR website!A rectangular field having an area of 2700 m^2 is to be enclosed by a fence, and an additional fence is to be used to divide the field in the middle. The cost of the fence down the middle is \$24 per running meter, and the fence along the sides cost \$36 per running meter. Estimate the dimensions of the field so that the total cost of the fencing material is least. : the area L * W = 2700 L = : The perimeter p = 2L + 2W + W; (3rd width down the middle) Cost = 36(2L) + 36(2W) + 24W C = 72L + 72W + 24W C = 72L + 96W Replace L with C = 72* + 96W C = + 96W Graph this: : looks like min cost occurs when the width is 45 meters then length = 2700/45 = 60 meters therefore 36(2*60) + 36(2*45) + 24(45) = \$8640 is the min cost