Quadratic equation word problem

Mar 2010
9
0
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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Mar 2010
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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 \(\displaystyle t\) be the number of weeks the grower waits, and let \(\displaystyle p\) be profit. So the equation is

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

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