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Math Help - Quadratic equation word problem

  1. #1
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    Quadratic equation word problem

    I'm trying to get a quadratic equation in general form from this word question:

    "A grower has 100 tonnes of potatoes that she can sell now for a profit of $500 per tonne. For each week that she delays shipment, she can produce an additional 10 tonnes of potatoes. However, for each week she delays, the profit decreases $25 a tonne."

    So I figured that if I could write all the information so that they are all related to the number of weeks (or as it relates to tonnes?) I could get a quadratic equation. There are questions like:

    a) when should she ship to maximize her profit, and what is the maximum profit?

    but if I just have the quadratic equation I can do the questions.. what I'm getting isn't working.

    Help would be much appreciated! Thanks!
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  2. #2
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    Quote Originally Posted by greatsheelephant View Post
    I'm trying to get a quadratic equation in general form from this word question:

    "A grower has 100 tonnes of potatoes that she can sell now for a profit of $500 per tonne. For each week that she delays shipment, she can produce an additional 10 tonnes of potatoes. However, for each week she delays, the profit decreases $25 a tonne."

    So I figured that if I could write all the information so that they are all related to the number of weeks (or as it relates to tonnes?) I could get a quadratic equation. There are questions like:

    a) when should she ship to maximize her profit, and what is the maximum profit?

    but if I just have the quadratic equation I can do the questions.. what I'm getting isn't working.

    Help would be much appreciated! Thanks!
    So the numbers look like this:

    Wait 0 weeks: 100 * 500 = 50000
    Wait 1 week: 110 * 475 = 52250
    Wait 2 weeks: 120 * 450 = 54000

    You can actually just calculate them all out and get to the maximum pretty quickly, but as for equation, let t be the number of weeks the grower waits, and let p be profit. So the equation is

    p = (100+10t) \cdot (500-25t)

    This is quadratic; from your post it seems that you know where to go from here.
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