EXAMPLE 14.1 A construction company has listed various activities that are involved in constructing a community hall. These are summarized along with predecessor(s) details in Table 14.1. Table 14.1 Details of Activities and Predecessor(s) for Constructing Community Hall Activity Description Immediate predecessor(s) A B D A B E F G H Plan approval Site preparation Arranging foundation materials Excavation for foundation Carpentry work for door and window main supporting frames Laying foundation Raising wall from foundation to window base Raising wall from window base to lintel level Roofing Electrical wiring & fitting Plastering Making doors and windows & fitting them White washing Clearing the site before handing over I J K L M N CD F EG H 1 JL A K M Draw a project network for the above project. 16.2 DEVELOPMENT OF LP MODELS Modelling is an art. One can develop this expertise only by seeing more and more models. In this section, the concept of model building is demonstrated using two example problems. EXAMPLE 16.1 A company manufactures two types of products, P1 and P2. Each product uses a lathe and milling machine. The processing time for Pl on the lathe is five hours and on the milling machine it is four hours. The processing time for P2 on the lathe is 10 hours and on the milling machine it is four hours. The maximum number of hours per week available on the lathe and the milling machine are 60 hours and 40 hours, respectively. The profit per unit of selling Pl and P2 are Rs. 6.00 and Rs. 8.00, respectively. Formulate a linear programming model to determine the production volume of each product such that the total profit is maximized. 199