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Math Help - Linear Programming Word Problem; system of inequalities

  1. #1
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    Linear Programming Word Problem; system of inequalities

    A hospital dietician wishes. To prepare a corn-squash vegetable dish that will provide at least 3 grams of protein and cost no more that .36 per serving. And ounce of cream corn provides 1/2 gram of protein and costs .04. An ounce of squash supplies 1/4 gram of protein and costs .03. For taste, there must be at least 2 ounces of corn and at least as much squash as corn. It is important to keep the total number of ounces in a serving as small as possible. Find the combination of corrn and squash that will minimize the amount of ingrediants used per serving. I am horrible at word problems and I've been trying to get the hang of it, please help.
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  2. #2
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    Re: Linear Programming Word Problem; system of inequalities

    Let "C" be the number of oz of creamed corn and "S" be the number of oz of squash, per serving.

    "ounce of cream corn provides 1/2 gram of protein" and "An ounce of squash supplies 1/4 gram of protein" so C oz of corn and S oz of squash provide C/2+ S/4 grams of protein.
    "provide at least 3 grams of protein" so you must have C/2+ S/4\ge 3

    And ounce of cream corn costs .04" and "An ounce of squash costs .03" so C oz of corn and S oz of squash cost .04C+ .03S.
    "cost no more that .36 per serving" so you must have .04C+ .03S\le .36.

    "For taste, there must be at least 2 ounces of corn and at least as much squash as corn." so C\ge 2 and S\ge C.

    "minimize the amount of ingrediants used per serving"
    Minimize C+ S.
    Last edited by HallsofIvy; April 23rd 2012 at 10:46 AM.
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  3. #3
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    Re: Linear Programming Word Problem; system of inequalities

    Thank you! That's what I thought. What equation do I use to find the min and max values?
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  4. #4
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    Re: Linear Programming Word Problem; system of inequalities

    Oh, nevermind! I got it (:
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