## Operations research: applications and algorithms |

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Page 10

x y w z

be thought of as a column

dimension of the column

...

x y w z

**VECTORS**Any matrix with only one column (that is, any m x 1 matrix) maybe thought of as a column

**vector**. The number of rows in a column**vector**is thedimension of the column

**vector**. Thus, 1 2 may be thought of as a 2 x 1 matrix or a...

Page 12

For the scalar product of two

then u • v = 1(2) + 2(1) + 3(2) = 10. By these rules for computing a scalar product,

...

For the scalar product of two

**vectors**to be defined, the first**vector**must be a row**vector**and the second**vector**must be a column**vector**. For example, if [1 2 3] andthen u • v = 1(2) + 2(1) + 3(2) = 10. By these rules for computing a scalar product,

...

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DEFINITION Suppose we are given a set V = {v,, v2, . . . ,vk} of w-dimensional row

whether V is a linearly independent set of

combination ...

DEFINITION Suppose we are given a set V = {v,, v2, . . . ,vk} of w-dimensional row

**vectors**. Let 0 = [0 0 • □ □ 0] be the m-dimensional 0**vector**. To determinewhether V is a linearly independent set of

**vectors**, we try to find a linearcombination ...

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### Contents

BASIC LINEAR ALGEBRA | 9 |

l | 42 |

INTRODUCTION TO LINEAR PROGRAMMING | 51 |

Copyright | |

24 other sections not shown

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### Common terms and phrases

annual assume basic feasible solution basic variable basis remains optimal choose coefficient in row concave function constraint convex function convex set current basis remains Dakota problem decision maker decision variables decrease demand determine dual enter the basis example feasible region Figure following LP Formulate an LP Giapetto goal goal programming Golden Section Search holding cost increase integer programming investment labor LINDO output linear programming lottery LP relaxation matrix max problem maximize maximum maximum flow problem maxz method minimize minimum node nonbasic variable nonnegative objective function coefficient obtain optimal solution optimal tableau optimal z-value Powerco primal PROBLEMS GROUP profit programming problem purchased random variable reorder point requires right-hand side row player satisfy Section shadow price Shapley value Show shown in Table simplex algorithm Step subproblem Suppose Test Market Theorem utility function vector yields zero