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
 
 The length of the brick fence that will minimize the cost of enclosing the playground is:
 x = 37.6 feet

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