Maximizing Profit from Crop Allocation

A local farmer is planting two types of crops: corn and wheat. The number of acres dedicated to corn can be represented by the variable $x$, and the number of acres for wheat can be represented by $y$. The farmer has a total of 100 acres available for planting.

The total profit from corn is modeled by the equation: $$P_1 = 200x$$

And the total profit from wheat is modeled by the equation: $$P_2 = 150y$$

Due to market demands, the farmer must allocate at least 20 acres to corn. Therefore, the system of equations can be expressed as:

$$x + y = 100$$

$$x \geq 20$$

What is the maximum total profit the farmer can achieve by optimally distributing the acres between corn and wheat?