you have the following goods:
$200$ apples
$350$ bananas
$200$ oranges
$600$ grapes
$400$ melons
Your goal is to receive back $400$ apples, $700$ bananas, $400$ oranges, $1200$ grapes, and $800$ melons in as few trades as possible. (double each good class)
rules/conditions:
The market will trade you any good you want for any other. (you can trade apples for bananas, oranges, grapes, or melons)
You may trade your goods for half as much up to twice as much as what you offered. (ex. $20$ apples can be traded for $10-40$ bananas)
- You trade your goods and once they are traded, they are gone (ex. you have $20$ apples you trade $10$ apples for $20$ bananas, you have $10$ more apples to trade with)
- You don't receive anything back until all trading is completed
- You can only trade whole numbers (no trading half a banana)
/ show the equation needed to derive the amounts needed of what for what