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Math Help - Help! This is confusing!

  1. #1
    Newbie Corky5's Avatar
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    Help! This is confusing!

    The AC Telephone Company manufactures two styles of cordless telephones, deluxe and standard. Each deluxe telephone nets the company $9 in profit, and each standard telephone nets $6. Machines A and B are used to make both styles of telephones. Each deluxe telephone requries three hours of machine A time and one hour of machine B time. An employee has an idea that frees twelve hours of machine A time and eight hours of machine B time. Determine the mix of telephones that can be made during this free time that most effectively generates profit for the company within the given restraints.

    Plese Help! It is really hard and confusing@
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  2. #2
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    Hello, Corky5!

    It's confusing to me, too . . . You left out part of the problem.

    Each standard telephone requires __ hours on machine A and __ hours on machine B.

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  3. #3
    Newbie Corky5's Avatar
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    Sry... here is the part i left out-Each standard telephone requires two hours of machine A time and two hours of machine B time....Thx
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  4. #4
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    Hello, Corky!

    The AC Telephone Co. makes two styles of cordless telephones: Deluxe and Standard.
    Each deluxe telephone nets the company $9 in profit, and each standard telephone nets $6.

    Machines A and B are used to make both styles of telephones.
    Each Deluxe telephone requries three hours on machine A and one hour on machine B.
    Each Standard phone requires 2 hours on machine A and two hours on machine B.

    An employee has an idea that frees 12 hours of machine A time and 8 hours of machine B time.
    Determine the mix of telephones that can be made during this free time
    that most effectively generates profit for the company within the given restraints.

    This is a linear programming problem.
    I'll assume you are familiar with the required knowldge.

    Let x = number of Deluxe phones to be made: . x \geq 0 [1]
    Let y = number of Standard phones to be made: . y \geq 0 [2]

    The x Deluxe phone take 3x hours on machine A and x hours on machine B.

    The y Standard phones take 2y hours on machine A and 2y hours on machine B.


    Maximum time on machine A is 12 hours: . 3x + 2y \:\leq\:12 [3]

    Maximum time on machine B is 8 hours: . x + 2y \:\leq \:8 [4]


    Graph the region determined by [1], [2], [3] and [4]
    . . and consider the vertices.
    Code:
            |
           6*
            | *
            |   *
       (0,4)o     *
            |:::*   *
            |:::::::* *
            |:::::::::::o (2,3)
            |:::::::::::::* *
            |:::::::::::::::*   *
            |:::::::::::::::::*     *
          - + - - - - - - - - - o - - - * - -
          (0,0)               (4,0)     8

    We have the vertices: . (0,0),\:(4,0),\;(2,3),\:(0,4)

    Test them in the profit function: . P \:=\:9x + 6y
    . . and see which produces maximum profit.

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