A company produces two types of products, A and B. The profit for each unit of product A is $10, and for each unit of product B is $15. The company can produce a maximum of 100 units of product A and 80 units of product B due to resource constraints. The total production cost for producing \( x \) units of product A and \( y \) units of product B is given by \( 3x + 5y \leq 400 \) dollars. Find the maximum profit the company can achieve. Let's think step by step and output the final answer within \boxed{}.
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