algebra

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OLD MCDONALD IS GOING TO PUT A PIG PEN UP AGAINST HIS BARN. HE HAS 45 FEET OF FENCING AND WILL ONLY NEED TO MAKE 3 ADDITIONAL SIDES, AS THE BARN ACTS AS THE FOURTH SIDE.. WHAT IS THE MAXIMUM AREA THAT THE PIG PEN CAN HAVE.

  • algebra -

    area = x * y

    x + 2y = 45 ... x = 45 - 2y

    substituting ... a = 45 y - 2 y^2

    ymax = -b / 2a = -45 / (2 * -2) = 11.25

    x = 22.5

    a = 22.5 * 11.25 = 253.125

  • algebra -

    or,
    by Calculus


    short side --- x
    single long side --- y
    2x + y = 45
    y = 45-2x

    Area = A = xy = x(45-2x)
    = 45x - 2x^2
    dA/dx = 45 - 4x = 0 for a max of A
    4x = 45
    x = 45/4 , then y = 45-2(45/4) = 45/2

    max area = xy = (45/4)(45/2)
    = 2025/8
    = appr 253.125 , same as Scott

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