J&J Watch Co is a well-known luxury watch manufacturer based in the United States. They produce only 3 different watch models; automatic, quartz and solar watches. To fulfil demand, it has to produce at least 5,000 automatics and 12,000 solar watches each year. From the past demand, they know that it only makes sense to produce at most 30,000 quartz watches in a year. J&J has two factories: one in Michigan, and another in Wisconsin; each factory is open for a maximum of 240 days per year. The Michigan factory makes 20 automatics, 40 solar, and 60 quartz watches per working day. The Wisconsin factory makes 10 automatics, 30 solar, and 50 quartz watches per working day. The cost to run the Michigan factory per day is $960,000; the cost to run the Wisconsin factory per day is $750,000. How many days of a year should each factory run in order to meet the watch demand at a minimum cost? (a) Develop the complete linear programming model that best captures the case. Clearly state decision variables, the objective function and constraints. (b) Using the graphical method, shade the feasible region, solve for all the corner points and identify the optimal solution. (Note that there is no need to use graph paper, you can draw on the answer booklet and solve it using corner point approach) (c) Provide any two applications of linear programming.