Linear Programming: Brass Ltd - Assignment Example

Summary Brass Ltd. is in need of an optimal solution to its product manufacturing problem. The problem involves manufacturing of two products amid a number of constraints such as availability of capacity, regulations on maximum output and controlled selling prices. The purpose of the report is to find an optimal solution to this problem using a linear programming model. The model has been solved using excel solver and the optimal solution is obtained. Further, a sensitivity analysis has been used to consider the impact of capacity increase on profitability. The report concludes with a few recommendations. 1. Problem Statement 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. 2. Model Development Using the selling prices, hours required by each product for each operation and availability constraints, the given problem can be converted into a linear programming model. The constraints can be specified by the following inequalities: M + 2R < 700 2.5M + 2R < 1000 M < 400 R < 400 M > 0 R > 0 The objective function can be derived as: Z = 40M + 50 R = Maximum The coefficients of objective function are the values of profit per unit of each product and are calculated by subtracting the total costs from the selling price. Here, Z = Objective Function M = Number of Masso R = Number of Russo This model can be developed in Excel as shown in Figure 3.1.   Masso Russo Total   Constraint Maximum Machining Hours 1 2 3 Read More