A company produces two types of products; Uni and Duo at its factories in Jinja and c) The optimal number of units for the company to produce each week can be Mbarara which are equipped with different types of machinery. At each factory, both shown to be; products undergo two production processes, machine hours available per week in each factory for both products are represented below; Jinja Mbarara Uni 7.5 16 Machine hours Duo 7.5 4 Jinja Mbarara Process 1 300 300 Determine the optimal contribution and the resources used. Compare this with your Process 2 300 324 solution to (a) above and make a recommendation to management. The process times (in hours) for a unit of each type of product in each factory are; Jinja Mbarara Uni Duo Uni Duc Process 1 10 30 10 15 Process 2 30 10 18 9 In addition, each unit of Uni and Duo uses 14 units of raw materials. Currently, 196 units of raw materials per week are allocated to the Jinja Factory and 294 units per week are allocated to the Mbarara Factory. At the moment, the company can not get more than 490 units of raw materials. It is estimated that the contribution to fixed overheads and profit is UGX 300 Per Unit for the Uni and UGX 200 Per Unit of Duo. Required a) Formulate a linear programming model for each factory and assuming a profit maximization objective, obtain by graphical means the optimal solutions. Determine the amount of resources used at each factory. b) Formulate (but do not solve) a single linear programming model for the company as a whole so that the model will determine the optimal allocation of the 490 units of raw material between the two factories