Optimization

Word Problems

Farmer Brown plans to fence in a rectangular pasture adjacent to a river.  The pasture must contain 180,00 square meters in order to provide enough feed for the herd.  What dimensions would require the least amount of fencing if no fencing is needed along the river?

xy = 180000  »  y = (180000/x)

P=2x + y   » P=2x + 180000x-1

Remember "No fencing is needed along the river thats why there is not 2y.

P' = 2 - 180000/x²

2- (180000/x²) = 0

2x² = 180000  x²=90000 x=300 when y = 600

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