10. Assume that you are a business analyst in a manufacturing company. Your manager gave you a task to optimise scheduling of a project. You are asked to minimize the overall manufacturing time. There are three items to be manufactured and three different machineries are available to be used for the manufacturing task. Due to operational reasons every machinery can only be allocated to the manufacturing of one item. Every item can only be manufactured by one machine. Different machinery has different speeds in manufacturing different items. Let us say i and m represent item and machinery, respectively. i represents the first item i represents the second item and so on. m represents the first machine, m represents the second machinery and so on. The duration of manufacturing every item pertaining to every machinery is presented in the below table. (10+10=20 marks) i i i3 m1 5 4 3 m2 5 9 6 M3 3 4 6 In this problem the sequence of manufacturing is important. Items and should be manufactured before manufacturing item i3. a) Write the linear optimisation model for the company to make the best decision. b) Solve the model, present the results and interpret them. Hint: you can use a binary variable such as xim which can take values of zero and one. Let us say Xim 1 if machine m is engaged to manufacture item i otherwise xim = 0.