The sauerkraut restaurant is facing a staffing shortage, so we have decided to outsource the production and sale of the components of our party packages to other companies. We give these companies our raw materials, and each of the companies has a list of how many of each type of product they can produce based on the amount and type of raw materials we give to them. Each company has also listed the revenue we can get from the sale of what they produce, but since they have limited throughput, each company can only produce at most a fixed total number of combined products (sauerkraut, cake, and candles) in a given week. Also, since market supply is limited, for each of the three types of raw materials (cabbage, cake mix, wax), our restaurant is only able to procure at most some fixed amount (inkg) of each. Come up with an LP to maximize expected revenue in a given week. For simplicity's sake, you may assume anything in the problem is allowed to be fractional. (a) What variables will be included in your LP? For each give a brief (few words) description of its purpose (e.g. "number of hours the baking process is used") (b) What is your objective function? Briefly explain how you came up with it. (c) What constraints do you need, and why?
