Our company can only commit $4,225 to this project without going into debt. Also, since the greenhouse can only hold so many trees, we need to make sure that we’re spending no more than $100 per tree, otherwise we’ll operate at a loss. Edgar assured me this was possible — he even showed me how to do it — but he took most of his notes with him, and I’m no mathematical genius.

Here’s how the expenses add up: First, the cost of the greenhouse. Then, for each tree in the greenhouse you need $5 for a proper planter. But the more trees there are the easier it is tospread infection between them, so the cost of disinfecting a tree rises as the number of treesincreases. Specifically, disinfecting each tree costs the total number of trees in the greenhouse.
The one example Edgar shared that I managed to save goes like this: Suppose we plant 10trees. Then we’d spend $2,222 for the greenhouse, plus $50 for planters, plus $10 to disinfecteach of the 10 trees (meaning $100 for disinfecting the whole greenhouse). The total cost wouldbe $2,372. So far so good. But unfortunately, this comes to more than $237 per tree — that’s bad.

I tried figuring out what happens if we increase the number of trees, say to 100. In that case,the cost per tree improves but still is not acceptable at $127. The total cost would be an exorbitant$12,722. Although I’m not even sure these figures are correct. I’m hoping you can tell me.
When I showed these figures to Sabbling she threw a fit — swore I’m going to wreck thecompany.
Can you help me figure out the math that will meet this challenge?