b) A manufacture can produce three different products in a given month. Each product requires four operations, i.e. casting, grinding, assembly and testing. The profits of each product, the maximum number of processing hours available in a month for each operation and the amount of time required by each unit of product in each operation are given in the table below; (i) Formulate a linear programming model that will maximize the profit and state the assumptions you made under this model [5 marks] (ii) Use Simplex method the linear programming problem and clearly interpret the results obtained. [10 marks] (iii) Determine the dual problem to the linear programming problem you formulated in b(i), clearly state the dual variables. [ 5 marks] [Total: 30 marks]