Maximize Widget Production Type A Under Constraints

A company produces two types of widgets: A and B. The cost to produce each widget A is $5, and the cost to produce each widget B is $8. The company has a budget of $400 for production. If the company decides to produce x widgets of type A and y widgets of type B, the total cost can be represented by the equation:

$$ 5x + 8y ext{ } ext{(total production cost)} ext{ } ext{ is at most } 400 $$

Additionally, the company wants to produce at least 30 widgets in total. This can be represented by:

$$ x + y ext{ } ext{(total widgets produced)} ext{ } ext{ is at least } 30 $$

What is the maximum number of widgets of type A they can produce, given these constraints?