Maximizing Soybean Yield under Profit Constraints

A local farmer has two types of crops: corn and soybeans. The corn crop has a profit margin of $3 per bushel, and the soybean crop has a profit margin of $4 per bushel. If the farmer aims to produce a total profit of $300 from these crops, he knows that he can plant a maximum of 100 bushels of corn and 80 bushels of soybeans due to land constraints.

Let $x$ represent the number of bushels of corn planted, and $y$ represent the number of bushels of soybeans planted. Write an equation expressing the total profit in terms of $x$ and $y$. Then, determine the maximum number of soybeans he can grow while still achieving his total profit goal. Assume the farmer wants to plant as much soybeans as possible within the stated constraints.