The company MP inc. manufactures connecting rods, which are mechanical parts that are used in the engines of cars. The company produces two types of rods : type A (for ordinary engines) and Type B (for injection engines). The manufacturing process of the connecting rods is comprised of two main operations : machining and assembly. MP inc. has two factories that can manufacture its models of connecting rods. The following table summarizes the unitary times required (min./rod) for perform the machining and the assembly operations for each plant (note that these times vary according to the factory, given the differences in the equipment used) : Factory 1 Factory 2 Operations A B A B Machining 15 24 12 28 Assembly 33 25 34 27 The labour costs that are paid by the company are directly defined by the hours worked for each of the operations in each factory. Thus, the company has evaluated that each hour worked at machining costs 15.50$ and that each hour worked at assembly costs 17.25$. Also, MP Inc. plans its production on a monthly basis. For the next month of production, the company has established that it will have 100 hours and 125 hours for machining and assembly, respectively, for each its factories. The company, which has already received orders for 180 rods of Type A and 200 rods of Type B for the next month, wants to ensure that the total production of Type A rods still represents at least 35% of everything that is produced at MP inc. Question (a) A rod of Type A is sold for 55$ per unit and that a rod of Type B is sold 62$ per unit. Also, the company assumes it will be able to sell everything it produces. Propose an optimization model that will enable the company to plan its production for the next month in a way that it maximizes the total profit generated. Clearly define the decision variables, the objective function and the constraints of the model. Question (b) Using EXCEL's solver, find an optimal solution to the model obtained for the previous question

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Answer a Optimization Model Decision Variables Let x1 be the number of Type A rods produced Let x2 b... View the full answer