A company produces two products, A and B, using two machines, X and Y. The company has limited production time of 80 hours per week on machine X and 60 hours per week on machine Y. The company's profit per unit of product A is $10 and that of product B is $15. The production time required to manufacture one unit of product A is 4 hours on machine X and 3 hours on machine Y. Similarly, the production time required to manufacture one unit of product B is 2 hours on machine X and 4 hours on machine Y. Determine the number of units of product A and B that the company should produce to maximize its profit.

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