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Math Help - Constraints

  1. #1
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    Constraints

    A company manufactures two products, A and B, using two machines I and II. To manufacture a unit of product A requires 6 minutes on Machine I and 5 minutes on Machine II. To manufacture a unit of product B requires 9 minutes on machine I and 4 minutes on machine II. There are 5 hours of machine time available in each work shift on machine I and 3 hours on machine II. The company realises a profit of $5 on each unit of product A and a profit of $7 on each unit of product B. The company wishes to determine the combination of products A and B that will yield the most profit. Let x be the number of product A to be produced. Let y be the number of product B to be produced.

    The common constraints are x >= 0 and y >= 0


    The other constraints are

    6x + 9y <= 300 (constraint on machine I time)
    5x + 4 y <= 180 (constraint on machine II time)


    Can someone explain where the 300 and 180 came from?


    Thank you!
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  2. #2
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    Lexington, MA (USA)
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    Hello, studentme!

    Look at the units of time . . .


    A company manufactures two products, A and B, using two machines I and II.
    To make a unit of product A requires 6 minutes on Machine I and 5 minutes on Machine II.
    To make a unit of product B requires 9 minutes on machine I and 4 minutes on machine II.

    There are 5 hours (300 minutes) of machine time available in each work shift on machine I
    and 3 hours (180 minutes) on machine II.
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