Linear Programming . Optimal Output and Calculation of Shadow Prices Essay

Linear Programming . Optimal Output and Calculation of Shadow Prices Using Graphical Approach Manually - Essay Example manage its operations well. Brass Ltd. manufactures two types of products – Masso and Russo which incur machining and assembly costs in their production. There are constraints on the availability of machining and assembly hours which are 700 hours and 1000 hours respectively. The capacity is fixed and the cost on the same is incurred irrespective of the usage. The maximum allowed production of each product type is 400 units. The selling price and costs incurred for the two products are available. The time spent on each machine for each product is also available. The company needs to know the optimal production of each product type to maximize profit. It also needs to gauge the impact of increasing production marginally on the profitability. There are certain inherent assumptions involved while formulating the above Linear Programming Model. The first assumption is that the constraints and the objective function can be represented through linear equations. In other words, the constraints on machining hours, assembly hours and the maximum production are directly proportional to both the number of Masso and the number of Russo. The second assumption is that the production of Masso is independent of the production of Russo and hence the impact of their production on the constraints as well as the objective function is perfectly additive. The third assumption is that the immediate objective of the firm is to recover the variable costs on the manufacturing of the two products and therefore fixed costs of machining and assembly are not considered for model formulation. Ideally, these fixed costs are distributed over the number of products manufactured. For obtaining a solution to the above model, the 6 inequalities shown above are plotted on a graph as shown in Figure 4.1 (www.maths.unp.ac.za). The two constraints regarding machining and assembly hours are plotted as straight lines. The two constraints on the