 9.6.a: 0, 4
 9.6.1: In the process called ________, you are asked to find the maximum o...
 9.6.b: 2, 3
 9.6.2: One type of optimization strategy is called ________ ________.
 9.6.c: 5, 0
 9.6.3: The ________ function of a linear programming problem gives the qua...
 9.6.d: 0, 0
 9.6.4: The ________ of a linear programming problem determine the set of _...
 9.6.5: The feasible solutions are ________ or ________ the boundary of the...
 9.6.6: If a linear programming problem has a solution, it must occur at a ...
 9.6.7: Objective function
 9.6.8: Objective function
 9.6.9: Objective function:
 9.6.10: Objective function: Constraints:
 9.6.11: Objective function:
 9.6.12: Objective function: Constraints:
 9.6.13: Objective function:
 9.6.14: Objective function: Constraints:
 9.6.15: Objective function
 9.6.16: Objective function
 9.6.17: Objective function
 9.6.18: Objective function
 9.6.19: Objective function
 9.6.20: Objective function
 9.6.21: z 2x y
 9.6.22: z 5x y
 9.6.23: z x y
 9.6.24: z 3x y
 9.6.25: z x 5y
 9.6.26: z 2x 4y
 9.6.27: z 4x 5y
 9.6.28: z 4x y
 9.6.29: Objective function
 9.6.30: Objective function
 9.6.31: Objective function
 9.6.32: Objective function
 9.6.33: Objective function
 9.6.34: Objective function
 9.6.35: OPTIMAL PROFIT A merchant plans to sell two models of MP3 players a...
 9.6.36: OPTIMAL PROFIT A manufacturer produces two models of elliptical cro...
 9.6.37: OPTIMAL COST An animal shelter mixes two brands of dog food. Brand ...
 9.6.38: OPTIMAL COST A humanitarian agency can use two models of vehicles f...
 9.6.39: OPTIMAL REVENUE An accounting firm has 780 hours of staff time and ...
 9.6.40: OPTIMAL REVENUE The accounting firm in Exercise 39 lowers its charg...
 9.6.41: MEDIA SELECTION A company has budgeted a maximum of $1,000,000 for ...
 9.6.42: OPTIMAL COST According to AAA (Automobile Association of America), ...
 9.6.43: INVESTMENT PORTFOLIO An investor has up to $250,000 to invest in tw...
 9.6.44: INVESTMENT PORTFOLIO An investor has up to $450,000 to invest in tw...
 9.6.45: If an objective function has a maximum value at the vertices and yo...
 9.6.46: If an objective function has a minimum value at the vertex you can ...
 9.6.47: When solving a linear programming problem, if the objective functio...
 9.6.48: CAPSTONE Using the constraint region shown below, determine which o...
Solutions for Chapter 9.6: Linear Programming
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 9.6: Linear Programming
Get Full SolutionsChapter 9.6: Linear Programming includes 52 full stepbystep solutions. Since 52 problems in chapter 9.6: Linear Programming have been answered, more than 49205 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048474. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Iterative method.
A sequence of steps intended to approach the desired solution.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.