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Math Help - inequalities linear programming

  1. #1
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    inequalities linear programming

    Hello eveyone!

    two machines:
    type A costs 50 per day and needs one person to operate it,
    type B costs 20 per day and needs 4 people to operate it

    let x be the number of type A
    let y be the number of type B

    1. a contracter has a labour force of 64 people, explain why x+4y is less than or equal to 64
    2. a contractor can spend up to 1040 per day on hiring machines, explain why 5x+2y is less than or equal to 104

    thanks!
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  2. #2
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    I had a go, and obviously, x+4y has to be equal to or less that 64 because that is teh workforce.

    64 has factors, 2, 4,8,16,32. so if x=2, 4y must be 62, but we can't get 62 so x can never be 2. is x=4, 4y must be 60 so y =15

    -am i on the right lines? I can't see how I would manipulate the algebra to answer this one.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Sweeties View Post
    I had a go, and obviously, x+4y has to be equal to or less that 64 because that is teh workforce.
    Yes, and that is all that is needed to answer 1. What follows is waffle.

    64 has factors, 2, 4,8,16,32. so if x=2, 4y must be 62, but we can't get 62 so x can never be 2. is x=4, 4y must be 60 so y =15

    That those are the factors of 64 has nothing to do with what you then write.

    If x=2 then y=15 satisfies the constaint, so x can be 2 (at least as far as the workforce constraint is concerned.

    Now what are you trying to do? This is not answering either of the questions asked.


    RonL
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  4. #4
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    Quote Originally Posted by CaptainBlack View Post
    Yes, and that is all that is needed to answer 1. What follows is waffle.




    That those are the factors of 64 has nothing to do with what you then write.

    If x=2 then y=15 satisfies the constaint, so x can be 2 (at least as far as the workforce constraint is concerned.

    Now what are you trying to do? This is not answering either of the questions asked.
    .


    RonL
    OK, I haven't a clue how to answer this question. The waffle was me having a go at it.

    Here's me having aother go:

    x+4y < 64 (take < to mean less than or equal to plz)

    4y < 64-x

    y= (64-x)/4

    y= 16 -x/4

    substitute into original equaion:

    x+ 4(16-x/4) <64

    x+ 64 -x <64

    64 < 64

    I get 64 is less than or equal to 64. Stumped.
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  5. #5
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    Quote Originally Posted by Sweeties View Post
    Hello eveyone!

    two machines:
    type A costs 50 per day and needs one person to operate it,
    type B costs 20 per day and needs 4 people to operate it

    let x be the number of type A
    let y be the number of type B

    1. a contracter has a labour force of 64 people, explain why x+4y is less than or equal to 64
    2. a contractor can spend up to 1040 per day on hiring machines, explain why 5x+2y is less than or equal to 104

    thanks!
    The bold bit are the two questions.
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  6. #6
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    Quote Originally Posted by Sweeties View Post
    Hello eveyone!

    two machines:
    type A costs 50 per day and needs one person to operate it,
    type B costs 20 per day and needs 4 people to operate it

    let x be the number of type A
    let y be the number of type B

    1. a contracter has a labour force of 64 people, explain why x+4y is less than or equal to 64
    2. a contractor can spend up to 1040 per day on hiring machines, explain why 5x+2y is less than or equal to 104

    thanks!
    x+4y\leq64 because you only have 64 possible workers, as you mentioned. If x+4y>64, then you won't have enough workers to operate all of the machines.

    Similarly for the second question, you have 5x+2y\leq104. You get this because 50x+20y\leq1040, where the left side is the amount of money needed to operate the machine, and the right side is your budget. Since you cannot exceed $1040, you know the inequality to be true, and you can easily see that 50x+20y\leq1040\implies\frac{50}{10}x+\frac{20}{10  }y\leq\frac{1040}{10}\implies5x+2y\leq104.
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