A company produces three products, Product A, Product B, and Product C, that require the same machine for production. Product A can be sold for a profit of $5/unit, Product B can be sold for a profit of $3/unit, and Product C for a profit of $1/unit. Product A takes 1.5 hours to produce per unit on the machine, Product B takes 1 hour per unit to produce, and Product C takes 0.5 hours per unit. At least 2 units of each product must be produced per day to fulfill existing orders, but the marketing department estimates that it cannot sell more than 12 units of any product per day. How many units of each product should the factory produce per day (1.e. 24 hours) to maximize profit? Assume that units are continuous variables (such as gallons or cubic meters) so that you could produce and sell a non- Integer number of units per day