SOLUTION: A fence must be built to enclose a rectangular area of 45,000 ft squared. Fencing material costs $3 per foot for the two sides facing north and south and ​$6 per foot for the
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Question 1114168: A fence must be built to enclose a rectangular area of 45,000 ft squared. Fencing material costs $3 per foot for the two sides facing north and south and $6 per foot for the other two sides. Find the cost of the least expensive fence. Answer by ikleyn(52776) (Show Source):
The problem asks to minimize the sum 2*(3x + 6y) under the condition xy = 45000.
It is the same as to minimize the form x+2y under the condition xy = 45000.
Then x + 2y = = .
To find the minimum of this function of x, take the derivative and equate it to zero:
- = = 0,
and the root (the solution) is x = 300.
Answer. The dimensions x= 300 ft (north and south sides) and = 150 ft (other two sides) give the required minimum.
The minimum cost of the fence is 2*(3*300 + 6*150) = 3600 dollars.
