Suppose a company produces two types of products, A and B, with production costs of $8 and $12 per unit, respectively. The company has a total production budget of $100,000 and wants to produce at least 6,000 units of product A and 3,000 units of product B. Each unit of product A generates a profit of $15, while each unit of product B generates a profit of $18. Determine the number of units of each product the company should produce to maximize its profit.

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