can you check to make sure the correct answer is 2000, 3000, and 4000? need to make sure my process is correct

A manufacturer produces three products, A, B, and C. The profits for each unit of A, B, and C sold are $ 1, $ 2, and $ 3, respectively. Fixed costs are $ 19,000 per year, and the costs of producing each unit of A, B, and C are $ 4, $ 5, and $ 7, respectively. Next year, a total of9000 units of all three products is to be produced and sold, and a total profit of $ 17,000 is to be realized. If total cost is to be $ 65,000, how many units of each of the products should be produced next year?