Question

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.)

Answer 1

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