My brother in year 8 was given this scenario:
"You sell chairs and make sales at monthly intervals. You start with $16,000.
Each month, 17000 people buy chairs, The market average price for chairs is $72.
Chairs cost $40 each when you buy 400 or more, and 35 dollars each when you buy 1000 or more.
Premium chairs cost 45 dollars each when you buy 400 or more, and 40 dollars each when you buy 1000 or more.
Your business sets the price of chairs. The price must be between $24-$150. For every $4 under the market average, your business gains 0.5% of the market.
For each $0.50 over the market average, your business loses 0.05% of its customers when selling standard chairs, and 0.01% of its customers when selling standard chairs, and 0.01% of its customers when selling premium chairs.
For every 1000 chairs sold in a month, your business must pay an employee $5000.10% of sales must go to the government for GST.
Your business may take out one loan at a time. You can only loan out as much money as you currently have. The loan compounds monthly at a rate of 18% per month. You must pay the entire loan off in a single month. The loan will continue to compound until you repay it.
Make the most profit possible within a year "
I think the purpose of this was for them to try different strategies and play around with them to see what works best. However, I'm wondering how this could be optimized to give the best possible result. As the problem is very convoluted I assume one could maybe use a program to simulate different situations however I wouldn't know how to do this. Feel free to simplify the problem if you wish to try it (eg. Don't use GST, premium chairs, or loans). I'm interested to see how a situation with multiple variables (the price each year) can be optimized.