115 Views

Download Presentation
## The application of mathematics and the scientific

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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**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**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**Page 18:**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 1 in a single equation and a coefficient of 0 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**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**Summary of Giapetto Inc. (Page 49)**Toy Sell Costs Hours of labor/toy Demand price Raw Labor Carpenter Finish per week ______________________________________________ Soldier $27 $10 $14 1 hr 2 hr40 Train $21 $9 $10 1 hr 1 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**Formulation of Giapetto Problem:**O.F. Max Z = 3 X1 + 2 X2 S.T. 2X1 + X2 100 Finish X1 + X2 80 Carpenter X1 40 Soldier X1 , X2 0 Sign IE 416, Chap 3:2, July 98**Graphical solution of Giapetto Inc.**Page 58 of textbook