T & L Manufacturing produces 3 unique products: X, Y, and Z. The office manager has recently been approached by upper management and asked to create an optimal production schedule for the coming month. The office manager knows the following about products X, Y, and Z. There are 2 steps to the production of each product: Plating and Heating. The plating process coats the product in a substance that will eventually harden and protect the outside of the product. Once the product has been plated it is heated until the outer shell has reached a temperature high enough to harden the material used in plating. Due to production stage, the manufacturer needs to produce at least 1500 units for each product. If made in house they cost $2.20, $1.50, and $1.20. Products X, Y, and Z need 12 minutes, 20 minutes, and 6 minutes each of plating. Under the current staffing situation there is currently 1500 hours of plating available for the coming month. Products X, Y, and Z need 6, 12, and 3 minutes of heating. There are currently 1000 hours of heating available. Due to limited resources all three of the products may either be built on site or bought from another manufacturer. It costs $3.00, $2.80, and $2.20 to buy these products from another manufacturer. The demand for products X, Y, and Z in the coming month is 3000, 5000, and 4000. Develop a plan to minimize the total costs for the coming month.