Abc daycare wants to build a fence to enclose a rectangular playground. the area of the playground is 940 square feet. the fence along three of the sides costs $5 per foot and the fence along the fourth side, which will be made of brick, costs $10 per foot. find the length of the brick fence that will minimize the cost of enclosing the playground. (round your answer to one decimal place.)
The area is: A = x * y = 940 The cost equation is: C (x) = 10x + 15y Rewriting: C (x) = 10x + 15 (940 / x) C (x) = 10x + 14100 / x We derive the cost equation: C '(x) = 10-14100 / x ^ 2 We equal zero and clear x: 0 = 10-14100 / x ^ 2 14100 / x ^ 2 = 10 x ^ 2 = (14100) / (10) x = root ((14100) / (10)) x = 37.54996671 x = 37.6 feet The other dimension is: y = 940 / 37.6 y = 25 feet Answer: The length of the brick fence that will minimize the cost of enclosing the playground is: x = 37.6 feet
