Bread Papa Bakery is a bakery chain that sells bread to customers in Hong Kong. Bread Papa owns bakeries in four locations: Sha Tin, Tsuen Wan, Kwun Tung and Kwai Chung. Each bakery can bake up to 800,000 loaves of bread each year. The fixed cost of operating a bakery for one year at each site is $4.5 million in Sha Tin, $3.2 in Tsuen Wan, $3.8 in Kwun Tung and $4.3 in Kwai Chung. Assume the Bread Papa has three customers, whose demands each year are 400,000 loaves (customer 1); 500,000 loaves (customer 2); and 300,000 loaves (customer 3). The total cost of baking and shipping a load of bread to a customer is given in the following table. From Sha Tin Customer 1 To Customer 2 Customer 3 $8 $12 $7 Tsuen Wan $6 $9 $10 Kwun Tung $13 $8 $9 Kwai Chung $9 $13 $11 (a) Formulate an integer linear programming problem that can be used to minimize the total yearly costs of meeting demand. [Clearly define the decision variables. No need to further compute any solution.] (b) Consider the following additional constraints, and indicate how you can formulate each of them into your model. [Each constraint should be done independently.] i. If the Kwun Tung bakery is opened, then the Kwai Chung bakery cannot be opened. ii. At most three bakeries can be opened. iii. If neither the Tsuen Wan nor Kwai Chung bakeries is opened, then the Sha Tin bakery must be opened. iv. The total cost of baking and shipping a load of bread from Kwun Tung bakery to customer 3 is no longer a constant $9 but depends on the quantity shipped. If the quantity is fewer than 100,000 units, the cost is $9; if the quantity is greater than or equal to 100,000 units, then the unit cost is $7.