You own a wheat warehouse with a capacity of $20$ bushels. At the beginning of month $1,$ you have $6$ bushels of wheat. Each month, wheat can be bought and sold at the prices per one busbel shown in the above table. The sequence of events during each month is as follows: You observe your initial stock of wheat. You can sell any amount of wheat up to your initial stock at the current month's selling price. You can then buy as much wheat as you want, subject to the warehouse capacity. Determine how to maximize the profit earned over the next $10$ months.

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