SOLUTION: A fence must be built to enclose a rectangular area of 45,000 ft^2. Fencing material costs $1 per foot for the two sides facing north and south and ​$2 per foot for the other two

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Question 1192763: A fence must be built to enclose a rectangular area of 45,000 ft^2. Fencing material costs $1 per foot for the two sides facing north and south and ​$2 per foot for the other two sides. Find the cost of the least expensive fence.
The cost of the least expensive fence is ​$___?
  
please answer the blank space with solving. Thank you
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= the width of rectangle in ft, y= the length of rectangle in ft.
A fence must be built to enclose a rectangular area of 45000ft%5E2
xy=45000=>y=45000%2Fx%E2%80%8B
The cost of the fence is:
C=2%282x%29%2B1%282y%29
C=4x%2B2y

substitute y
C%28x%29=4x%2B2%2845000%2Fx%29, x+%3E+0

Find the first derivative with respect to x
C′%28x%29=4-90000%2Fx%5E2%E2%80%8B
Find the critical value(s)
C′%28x%29=0
4-90000%2Fx%5E2=0
=>x%5B1%5D=-150
=>x%5B2%5D=150

Since x%3E0, then the function C%28x%29 has the absolute minimum at x=150.
so, y=45000%2Fx=45000%2F150=300
and, the cost will be:
C=4%2A150%2B2%2A300=1200

The cost of the least expensive fence is ​$1200?