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Unformatted text preview: CHAPTER 2 LINEAR PROGRAMMING: BASIC CONCEPTS Review Questions 2.1-1 Ponderosa Industrial uses linear programming monthly to guide the product-mix decision. 2.1-2 Overall profitability has increased by 20%. Better utilization of raw material, capital equipment, and personnel also resulted. 2.1-3 The goal was to improve the utilization of reservation personnel by matching work schedules to customer needs. 2.1-4 United Airlines saved more than $6 million annually in direct salary and benefit costs. Customer service also improved and workloads were reduced for support staff. 2.1-5 The SDM system is used to coordinate the supply, distribution and marketing of each of Citgos major products throughout the United States. 2.1-6 Citgo saved about $14 million annually in interest expenses. Improvements in coordination, pricing, and purchasing decisions added at least $2.5 million more to annual profits. 2.2-1 They provide the highest quality available in the industry for the most discriminating buyers. 2.2-2 1) Should the company launch the two new products? 2) What should be the product mix for the two new products? 2.2-3 The group was asked to analyze product mix. 2.2-4 Which combination of production rates for the two new products would maximize the total profit from both of them. 2.2-5 1) available production capacity in each of the plants 2) how much of the production capacity in each plant would be needed by each product 3) profitability of each product 2.3-1 1) What are the decisions to be made? 2) What are the constraints on these decisions? 3) What is the overall measure of performance for these decisions? 2.3-2 When formulating a linear programming model on a spreadsheet, the cells showing the data for the problem are called the data cells. The changing cells are the cells that contain the decisions to be made. The output cells are the cells that provide output that depends on the changing cells. The target cell is a special kind of output cell that shows the overall measure of performance of the decision to be made. 2.3-3 The Excel equation for each output cell can be expressed as a SUMPRODUCT function, where each term in the sum is the product of a data cell and a changing cell. 2-1 2.4-1 1) Gather the relevant data. 2) Identify the decisions to be made. 3) Identify the constraints on these decisions. 4) Identify the overall measure of performance for these decisions. 5) Convert the verbal description of the constraints and measure of performance into quantitative expressions in terms of the data and decisions 2.4-2 Algebraic symbols need to be introduced to represents the measure of performance and the decisions. 2.4-3 A decision variable is an algebraic variable that represents a decision regarding the level of a particular activity. The objective function is the part of a linear programming model that expresses what needs to be either maximized or minimized, depending on the objective for the problem. A nonnegativity constraint is a constraint that express the restriction that a...
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- Spring '10