A company produces two types of products, A and B. The profit from one unit of product A is $40, and the profit from one unit of product B is $30. The company can produce a maximum of 200 units of both products combined per week. Additionally, the company must produce at least 50 units of product A and at least 30 units of product B each week. How many units of each product should the company produce to maximize its profit? Also, determine the maximum profit. Let's think step by step and output the final answer within \boxed{}.
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