LESSON III (4 Hours) AN INTRODUCTION TO LINEAR PROGRAMMING Linear Programminguses a mathematical model to represent the problem being studied. The word linearin the name refers to the form of mathematical expressions in this model. Programmingdoes not refer to computer programming; rather, it is essentially a synonym for planning. Thus, linear programming means the planning of activities represented by a linear mathematical model. 3.1 SIMPLE MAXIMIZATION PROBLEM Par, Inc., is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium and high-priced golf bags. Par Inc.’s distributor is enthusiastic about the new product line and has agreed to buy all the golf bags Par, Inc., produces over the next three months. After a thorough investigation of the steps involved in manufacturing a golf bag, management determined that each golf bag produced will require the following operations: 1. Cutting and dyeing the material 2. Sewing 3. Finishing (inserting umbrella holder, club separators, etc. ) 4. Inspection and packaging The production information is summarized in Table 3.1. Par Inc.’s production is constrained by a limited number of hours available in each department. After studying departmental workload projections, the director of manufacturing estimates that 630 hours for cutting and dyeing, 600 hours for sewing, 708 hours for finishing and 135 hours for inspection and packaging will be available for the production of golf bags during the next three months. The accounting department analyzed production data, assigned all relevant variable costs, and arrived at prices for both bags that will result in a profit contribution of P10.00 for evrery standard bag and P9.00 for every deluxe bag produced. TABLE 3.1. PRODUCTION REQUIREMENTS PER GOLF BAG Production Time ( in hours) Department Standard Bag Deluxe Bag Cutting and Dyeing 7/10 Sewing ½ 5/6 Finishing 1 2/3 Inspection and Packaging 1/10 1/4 1
PROBLEM FORMULATION Problem Formulation or Modeling- is the process of translating the verbal statement of a problem into a mathematical statement. Formulating models is an art that can only be mastered with practice and experience.