anonymous
  • anonymous
A farmer is building a rectangular, three-sided fence next to a river. One of the sides is $15/foot while the other two are $10/foot. The area must be 1.6 million square feet. Find the dimensions that minimize the cost of the fence.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[C=10x+15y+15y =10x+30y \] use A=xy=1.6 to solve for y in terms of x then substitute into the cost function , take the derivative and find the critital points the minimal will occur at the critical point
anonymous
  • anonymous
I plug the critical points back into the Cost of Area equation ?
anonymous
  • anonymous
*cost or area

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anonymous
  • anonymous
\[y=1,600,000/x\] substitute this into the cost function for y. then take the derivative of the cost function
anonymous
  • anonymous
sorry the cost function is \[C=20x +15y\]
anonymous
  • anonymous
So you end up with C = 20(1,600,000/y) + 15y
anonymous
  • anonymous
which is C = 32,000,000/y + 15y
anonymous
  • anonymous
WOULD THE area be A=xy or A=2xy

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