Download Linear Programming: A Case Study of GTMC's Production and Raw Material Management - Prof. and more Assignments Mathematics in PDF only on Docsity! Name: Introduction to Linear Programs MA 416 1. Understanding the Variables (a) The Problem The following problem was adapted from an example in Chapters 6 and 7 of Carl Lee’s MA 515 notes. The notes were for the course he taught in the Fall of 2007. The can be found at: http://www.ms.ukjy.edu/∼lee/ma515f07/notes.pdf The Gadgets and Trinkets Manufacturing Company (GTMC) manufactures gadgets and trinkets. To man- ufacture one gadget, GTMC uses one hour of labor, one unit of wood, and two units of metal. To manufacture one trinket, GTMC uses two hours of labor, one unit of wood and one unit of metal. The production manager and the comptroller have seemingly different goals, but they must work together to make profitable decisions for GTMC. There are 120 hours of labor, 70 units of wood, and 100 units of metal available. i. The Production Manager. The production manager runs the factory of GTMC. The job of the produc- tion manager is to determine the number (x1) of gadgets and the number (x2) of trinkets that should be produced. In today’s market, each gadget sells for $45, each trinket for $59, each hour of labor costs $20, each unit of wood $10, and each unit of metal $5. A. Assuming that every gadget produced will be sold, what is the net profit of producing x1 gadgets and x2 trinkets? B. Common sense tells us that the production manager wants to the net profit. C. Based on the problem description, what restrictions are placed on the production manager? ii. The Comptroller, i.e. The Warehouse Manager The Comptroller is in charge of the raw materials. In this example, we have a specified amount of labor, wood, and metal in the warehouse. (Technically, the labor is not in the warehouse, but it is a commodity that we could, in theory, sell. To simplify the discussion, we will assume that there is a shelf in the warehouse devoted to labor.) The production assistant will use some of these raw materials to produce gadgets and trinkets, but not all of them. (Can you explain this observation?) Raw materials that remain in the warehouse are a lost opportunity. Perhaps another company would be willing to purchase GTMC’s resources. The job of the Comptroller is to set the prices for the raw materials. If another company offers to purchase the raw materials at these prices, GTMC will sell them. Assume that w1 is the price set for one hour of labor, w2 is the price set for one unit of wood, and w3 is the price set for one unit of metal. A. What is the lost opportunity cost of keeping all of our materials in the warehouse and producing nothing? B. Common sense tells us that the comptroller wants to the lost opportunity cost. C. What restriction(s) do the current market prices of the raw materials place on the comptroller? D. What restriction(s) do the current market prices of the gadgets and trin- kets place on the comptroller?
