A rectangular field is to be enclosed with a fence. One side of the field is aga

Question

A rectangular field is to be enclosed with a fence. One side of the field is against an existing fence, so that no fence is needed on that side. If material for the fence cost $6 per foot for the two ends and $8 per foot for the side parallel to the existing fence, find the dimensions of the field of the largest area that can be enclosed for $3,000.

Explanation / Answer

cost function 2*6*x+8*y=3000 ==>3x+2y=750 area=x*y =x(750-3x)/2 =(750x-3x^2)/2 derivative=0 ==>750-6x=0 ==>x=750/6 ==>x=125-------->length of each end 2y=750-375 y=187.5-------->length of the side parallel to the existing fence

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