Question: A company produces three products from raw material and the other products. Each pound of raw material undergoes processing and yields 3 ounces of product 1 and 1 ounce of product 2. Each pound of raw material costs $25 to purchase and takes 2 hours of labor to process. Each ounce of product 1 can be handled in one of three ways. First, it can be sold for $10 per ounce. Second, it can be processed into 2/3 ounces of product 2. This requires 2 hours of labor and costs and additional $1. Third, it can be processed into 1/2 ounces of product 3. This requires 3 hours of labor and costs an additional $2. Each ounce of product 2 can be used in one of two ways. First, if can be sold for $20 per ounce. Second, it can be processed into 3/4 ounces of product 3. This requires 1 hour of labor and costs $6 more. Product 3 is sold for $30 ounce. The maximum numbers of ounces of products 1, 2, and 3 that can be sold are, respectively, 5000, 4000, and 3000. A maximum of 25,000 hours of labor are available.
(a) Write down a linear programming model that maximizes the company's profit. You do not need to write a data-independent model, a specific model for this particular instance with numbers is fine.