Maximizing Cake Production

A bakery produces a variety of cakes. Let the variable $x$ represent the number of chocolate cakes produced and $y$ represent the number of vanilla cakes produced. The bakery has determined that the total number of cakes produced is at most 200, which can be expressed using the inequality:

$$x + y \leq 200$$

Additionally, the bakery has a specific production ratio of chocolate cakes to vanilla cakes, such that the number of chocolate cakes produced is at least three times the number of vanilla cakes produced, represented by the inequality:

$$x \geq 3y$$

To maximize the total production while adhering to both inequalities, how many chocolate cakes is the bakery able to produce if they produce the maximum feasible number of vanilla cakes?