Chapter 2 Flashcards
Linear Programming Model Objective
Maximize or Minimize and linear objective function subject to set of linear constraints
Characteristic of LPM (4)`
decision variables
linear objective function
linear constraints
non negative decision variables
Objective function (2)
maximize profit or minimize cost
Applicability
real world applications of LPM
Solvability
theoretically and practically efficient techniques for solving large scale problems
LP is central topic in…..
optimization
Standard form
all system constraints written as equalities
Optimal solution of standard form and optimal solution of Linear programming model
they are equal
Slack variable
what is
when added
symbol
amount of unused resource
added to left side of equation when less than or equal to <=
+S
Surplus variable
what is
when added
symbol
amount over and above required amount
added to left side of equation when greater than or equal to >=
-S
Cost of surplus and slack is
0 zero
Binding constraint (3)
passes through optimal solution
left hand side of equation = right hand side of equation for constraint
slack/surplus = 0
Non-Binding Constraint (3)
does not pass through optimal solution
left hand side and right hand side are unequal of constraint
slack/surplus > 0
binding is also called ____ constraint
active
non binding is also called _____ constraint
non-active
Graphical solution possibilites (3)
one feasible solution
no feasible solution
infinite number of feasible solutions
Feasible Solution and where on graph
satisfies all constraints, area on graph bounded
feasible region
set of all possible feasible solutions, contains all feasible and optimal solutions
infeasible
no feasible solutions, region is empty
Optimal solution
best possible value of objective function, best feasible solution
Linear program model may have _______ _______ solutions but only ______ ________ solution value
Linear program model may have multiple optimal solutions but only one optimal solution value
optimal solution mazimize
last point objective function touches as it leave feasible solution area (away from origin)
optimal solution minimize
extreme point closest to the origin
Alternative Optimal Solution
more than one solution provides optimal value for objective function
unbounded
value of solution is made infinitely large in a maximize problem or infinitely small in minimize problem without violating constraints
Extreme points
vertices or corners of feasible region
