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Thread: Need guidance working through an optimization equation with three variables

  1. #1
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    Need guidance working through an optimization equation with three variables

    Hello All,

    Thanks in advance for taking the time to read this and trying to help.

    I am working through an optimization problem, I have three variables and one constraint. My mathematical background doesn't go beyond high school calculus and I was never particularly adept so I'm hoping that whatever explanation is offered explains the issue to me like the math simpleton that I am. The problem is as follows:

    I am trying to optimize the number of units of three different products that are sold at three different prices. We have a target revenue figure, meaning we know what we want the final equation to sum upto but unlike the simple substitution method one would apply to two variables I am at a loss for what to do for three.

    175X + 225Y + 500Z = 7385, where
    X+Y+Z=18

    Look forward to your responses, if you need further information or I've misunderstood something please feel free to ask and I'll do my best to clarify.
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  2. #2
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    Re: Need guidance working through an optimization equation with three variables

    You've specified the target revenue and the number of items made.

    What exactly are you trying to optimize?

    You have one degree of freedom in this setup.

    But there is nothing here that distinguishes one value of that dof as being more optimal than another.
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  3. #3
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    Re: Need guidance working through an optimization equation with three variables

    ok I guess this could be interpreted as

    $175x + 255y + 500z \geq 7385$

    $x+y+z=18$

    if this is the case the trivial solution to optimize revenue is $x=y=0,~z=18$

    This leads to a revenue of $9000$ which exceeds your target.

    Somehow I think there is more to the problem than this.
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  4. #4
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    Re: Need guidance working through an optimization equation with three variables

    There are 20 ways to exceed 7385;
    0,0,18 = 9000 (high) as per Romsek
    to
    4,1,13 = 7425 (low) as per yours untruly!
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  5. #5
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    Re: Need guidance working through an optimization equation with three variables

    In general, you need three pieces of information to solve a problem with two unknowns. You have given two.
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