A company produces two products, P and Q. The cost to produce product P is given by the equation $$C_P(x) = 4x + 50$$, where $$x$$ is the number of units produced. The cost to produce product Q is given by the equation $$C_Q(y) = 6y + 30$$, where $$y$$ is the number of units produced. If the company has a total budget of $$500$$ to produce both products combined, what is the maximum number of units of product P that can be produced if 20 units of product Q are produced?