Linear Programming Assignment Example | Topics and Well Written Essays - 1250 words

Linear Programming - Assignment Example Brass Ltd. manufactures two products named Masso and Russo. These products require machining and assembly hours for their production. The available capacity of each of these hours is limited. Also there are government controls on the maximum output of each type. Under these constraints, the company needs to develop an optimal production plan. The company also needs to know the impact of marginal increase in the constraints on its profitability. The selling prices of the products are also controlled by the government though demand is unfulfilled. The first assumption of the above model is the assumption of independence. This implies that the production of both products is independent of each other and so is their impact on the number of machining or assembly hours. Therefore, the two effects can be added to each other. The second assumption is the assumption of linearity. In other words it is assumed that a linear relation exists between the number of products and machining or assembly hours. This assumption makes possible the use of linear programming model for the given problem. The optimal solution can be obtained by solving the above model through Excel solver as shown in Figure 4.1 (Taha, 2009). In the beginning, the number of products of each type is taken as 1. The objective function value is the decision variable as it needs to be maximized. The number of products is the output variable while the constraints are given by the various inequalities. Sensitivity analysis is performed to notice the impact of a marginal increase in the value of machining hours and assembly hours on the objective function. From the figure, it can be noticed that when the available capacity of machining hours is changed from 700 to 701 hours, the profit increases by $15. When the available capacity of assembly hours is changed from 1000 to 1001 hours, the profit increases by $10. This increase in profit with marginal relaxation of