A rancher wishes to build a fence to enclose a rectangular pen having area 24 square yards. Along one side the fence is to be made of heavy duty material costing $6 per yard, while the remaining three sides are to be made of cheaper material costing $3 per yard. Determine the least cost of fencing for the pen.

The  value  is  

Step-by-step explanation:

From the question we are told that

   The  area of the rectangular pen is  

     The  cost of material used to make one side is  

    The  cost of material used to make the other sides is  

Now  , the fence to be build around the rectangular pen  has four sides, the first opposite sides are equal, let assume each of the to be x yard   and the other opposite sides are also equal as well let assume of the to be y yard

So the cost is mathematically represented as

=>  

=>  

Now the area of the fence is mathematically represented as

=>    

=>  

=>  

Now differentiating

At minimum

So  

Now substituting for x in the equation above to obtain minimum cost

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step-by-step explanation: vsfdvsfvd

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