文档介绍：Linear Programming Using Excel Solver
Operations Management
petitive Advantage
CHASE AQUILANO JACOBS
ninth edition
Supplement A
Supplement A Linear Programming Using Excel Solver
Linear Programming
A Maximization Problem
A Minimization Problem
Linear Programming
Is used in problems where resources are constrained or limited.
The model has an objective (function)
Generally maximizing profit or minimizing costs subject to resource-based, or other, constraints.
Linearity is a requirement of the model in both objective function and constraints.
Variables must be divisible (., permit fractional values if need be) and non-negative.
Objective Function
Maximize (or Minimize) Z = C1X1 + C2X2 + ... + CnXn
Cj is a constant that describes the rate of contribution to costs or profit of units being produced (Xj).
Z is the total cost or profit from the given number of units being produced.
Constraints
A11X1 + A12X2 + ... + A1nXnB1
A21X1 + A22X2 + ... + A2nXn B2
:
:
AM1X1 + AM2X2 + ... + AMnXn=BM
Aij are resource requirements for each of the related (Xj) decision variables.
Bi are the available resource requirements.
Note that the direction of the inequalities can be all or bination of , , or = linear mathematical expressions.
Non-Negativity Requirement
X1,X2, …, Xn 0
All linear programming model formulations require their decision variables to be non-negative.
While these non-negativity requirements take the form of a constraint, they are considered a mathematical requirement plete the formulation of an LP model.
An Example of a Maximization Problem
LawnGrow pany must determine the mix of mercial riding mower products to be produced next year. pany produces two product lines, the Max and the Multimax. The average profit is $400 for each Max and $800 for each Multimax. Fabrication and assembly are limited resources. There is a maximum of 5,000 hours of fabrication capacity available per month (Each Max requires 3 hours and each Multimax requires 5