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anonymous

  • 5 years ago

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.

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  1. anonymous
    • 5 years ago
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    \[C=10x+15y+15y =10x+30y \] 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

  2. anonymous
    • 5 years ago
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    I plug the critical points back into the Cost of Area equation ?

  3. anonymous
    • 5 years ago
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    *cost or area

  4. anonymous
    • 5 years ago
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    \[y=1,600,000/x\] substitute this into the cost function for y. then take the derivative of the cost function

  5. anonymous
    • 5 years ago
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    sorry the cost function is \[C=20x +15y\]

  6. anonymous
    • 5 years ago
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    So you end up with C = 20(1,600,000/y) + 15y

  7. anonymous
    • 5 years ago
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    which is C = 32,000,000/y + 15y

  8. anonymous
    • 5 years ago
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    WOULD THE area be A=xy or A=2xy

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