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anonymous

  • 5 years ago

A pig rancher wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). He has 620 feet of fencing available to complete the job. What is the largest possible total area of the four pens? A=2x + 5y

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  1. anonymous
    • 5 years ago
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    radar, I sense that you already have solved this problem. Ami I wrong?

  2. radar
    • 5 years ago
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    I think you mean amount of wire used = 2x+5y then 5y=620-2x 5y=(620-2x) y=124-(2/5)x A=x(124-(2/5)x=124-(2/5)x^2 dA/dx=124-(4/5)x set to 0 x=155 ft y=62 ft pen will use 2(155) ft + 5(62) ft

  3. anonymous
    • 5 years ago
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    the pen has 5 y walls and 2 x walls

  4. radar
    • 5 years ago
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    yes and as I said, 5 62 ft walls and 2 155' walls

  5. anonymous
    • 5 years ago
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    not right you have to use the derivative of A= 2x+5y then solve for whats the greatest area im going to attach a picture.

  6. anonymous
    • 5 years ago
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  7. anonymous
    • 5 years ago
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    x = width, which is used 5 times to make 4 pens. (620 - 5x)/2 = length of pens y = x(620 - 5x)/2 y = 310x - 5/2x² The maximum area occurs at the vertex , which is at x = -b/(2a) = -310/-5 = 86 feet width (620- 5x)/2 - (620 - 5(62))/2 = 310/2 = 155 = combined width of all 5 pens 62 x 155 = 9610 ft² <==ANSWER

  8. anonymous
    • 5 years ago
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    i got it thanks

  9. radar
    • 5 years ago
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    Exactlly, what I had

  10. anonymous
    • 5 years ago
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    yes but i need greatest volume

  11. anonymous
    • 5 years ago
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    area*

  12. radar
    • 5 years ago
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    Didn't I give you the greatest area 62 x 155? The area would of been 9610 sq ft. What was the different asnwer?

  13. radar
    • 5 years ago
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    You are confusing me, I took the derivative of A for area, set it to 0 and got 62 and 155. Using the restraints on the amount of wire and separate pen requirements. What was done different?

  14. anonymous
    • 5 years ago
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    "pen will use 2(155) ft + 5(62) ft" you did + instead of x but its all in all right work,thanks

  15. radar
    • 5 years ago
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    Glad you now understand how to solve these kind of problems. Good luck with your study efforts.

  16. anonymous
    • 5 years ago
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    radar, It looks like everything worked out fine. Have a good day.

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