A company manufactures two types of widgets, A and B. The profit from selling one unit of widget A is $3, and the profit from selling one unit of widget B is $4. The production of each widget requires different amounts of resources. Producing one unit of widget A requires 2 hours of labor and 1 unit of material, while producing one unit of widget B requires 1 hour of labor and 2 units of material. The company has a total of 100 hours of labor and 80 units of material available. 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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