A cake bakery is planning to produce new cakes. The setup cost of the production facilities and the unit profit for each type of cake are given below. : cake type Setup cost () Profit () 1 2 45000 76000 12 16 The company has two factories that are capable of producing these types of cakes. In order to avoid doubling the setup cost only one bakery could be used. The production rates of each cake type are given below (in units/hour): bakery 1 bakery 2 cake type 1 cake type 2 52 42 38 23 Factories 1 and 2, respectively, have 480 and 720 hours of production time available for the production of these types of cake. The manufacturer wants to know which of the new cakes to produce, where and how many of each (if any) should be produced so as to maximise the total profit. Introducing 0-1 decision variables formulate the above problem as an integer program.