1. The application of mathematics and the scientific
method to military operations was called operations
research. Today, the term operations research (or,
often, management science) means a scientific
approach to decision making, .… under conditions
requiring the allocation of scarce resources.
IE 416, Chap 1:1, July 98

2. Different Representation of Linear System of Equations
Linear Equations:
Augmented matrix:
Compact form: A x = b
x =
b = A=
IE 416, Chap 2:1, July 98

3. Gauss-Jordan Method: Elementary Row Operation, ero
Page 20:
Gauss-Jordan Method:
Elementary Row Operation, ero
Type 1 ero: (Row i)' = C (Row i)
Type 2 ero: (Row i)' = C (Row j) + (Row i)
Type 3 ero: (Row i)' = (Row j)
(Row j)' = (Row i)
IE 416, Chap 2:3, July 98

4. A solution to a linear system of m equations in n
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A solution to a linear system of m equations in n
unknowns is a set of values for the unknowns that
satisfies each of the system's m equations.
For any linear system, a variable that appears
with a coefficient of in a single equation and
a coefficient of in all other equations is called
a basic variable (BV). Any variable that is not a
basic variable is called a nonbasic variable (NBV).
IE 416, Chap 2:2, July 98

5. Linear Programming Terms (Chap. 3) * Summarize the problem as a matrix
* Formulate the problem: decision variable, objective
function (OF), OF coefficient, constraint (ST),
technological coefficient, right hand side (RHS),
sign restriction, unrestricted in sign (URS),
assumptions (divisibility, certainty, … )
* Solve the problem: feasible region (based on
constraints, bounded, unbounded, no f.r.), graphical
solution, iso-profit (cost) line, optimal solution
(extreme point, no solution, one solution, multi-
solution), binding constraint, nonbinding constraint,
infeasible LP, unbounded LP
IE 416, Chap 3, May 99

6. Summary of Giapetto Inc. (Page 49)
Toy Sell Costs Hours of labor/toy Demand
price Raw Labor Carpenter Finish per week
______________________________________________
Soldier $27 $10 $ hr hr
Train $21 $9 $ hr hr no limit
no max 80 max 100
limit
X1 = number of soldiers / week
X2 = number of trains / week
IE 416, Chap 3:1, July 98

7. Formulation of Giapetto Problem: O.F. Max Z = 3 X1 + 2 X2
S.T. 2X1 + X2  Finish
X1 + X2  Carpenter
X  Soldier
X1 , X2  Sign
IE 416, Chap 3:2, July 98

8. Graphical solution of Giapetto Inc.
Page 58 of textbook