#### greatsheelephant

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!

#### undefined

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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.