高级管理会计Advanced Management Accounting 线性规划 Linear Programming.pptVIP

LOGO “ Add your company slogan ” Advanced Management Accounting * Linear Programming FOUNDATION REVIEW * Contents Interpreting linear programming results Solver application in Excel The linear programming model Graphing linear inequalities Overview * overview Linear programming is a mathematical technique that was developed to help managers make better decisions. It is called linear programming because it involves solving sets of simultaneous linear equations. The common theme to each problem is that one wants to minimize or maximize some quantity (usually cost or profit), which is the objective, within certain resource restrictions, which are called constraints. * resource constraints A Title marketing constraints C Title structural constraints B Title In general, there are three types of constraints: * Graphing linear inequalities EXAMPLE FR.1 2x1 + 3x2 = 10 3x1 – 4x2 = –2 EXHIBIT FR-2 EXHIBIT FR-3 EXAMPLE FR.2 3x1 – 4x2 ≤ –2. EXHIBIT FR-4 * Steps in linear programming Step 1: Determine the objective. What is the goal? Write the goal in terms of an equation.This equation is called the objective function. Step 2: Specify the constraints. Like the objective, each constraint needs to be written in the form of an equation, which will be either an equality or inequality. These equations are mathematical models of the relationships in the problem. Step 3: Compute the optimal solution. There are three approaches to computing the optimal solution: trial-and-error, graphic, and computer modelling. * The linear programming model EXAMPLE FR.3 The problem, accordingly, has been formulated as a linear programming model: Maximize 6x1 + 8x2 Subject to: 2x1 + 2x2 ≤ 1,600 2x1 + 4x2 ≤ 2,000 x2 ≤ 400 x1 ≥ 0, x2 ≥ 0 * In formulating the problem as a linear programming model, three necessary assumptions — Proportionality(同比例性), Divisibility(可分性), Additivity(可加性)