A farmer wants to fence in a rectangular plot in a large field, using a stone wa

Question

A farmer wants to fence in a rectangular plot in a large field, using a stone wall which is already there as the east oundary. The fence for the north and the south sides of the plot will cost $3/yard. On the west side of the plot, the farmer needs to use special fence which costs $5/yard. If the area of the plot is 60 square yards, find the farmer's minimal cost of the fencing.

So far I have gotten:

6x + 5y = C (Cost function)

xy = 60 (area of the field)

Solving for y: y = 60/x

Put that into the Cost function:

6x + 5(60/x) = C

6x + 300/x = C

And now I am stuck.

Explanation / Answer

C=6x + 300/x

to find minimum value of C , differentiate it

dC/dx = 6-300/x^2=0

x=sqrt(50) = 7.07

cost= 6*7.07 + 300/7.07 = $84.85

PLEASE RATE THE BEST ANSWER

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