 6.6.17: In Exercises 1720, use a graphing utility to graph the regiondeterm...
 6.6.18: In Exercises 1720, use a graphing utility to graph the regiondeterm...
 6.6.19: In Exercises 1720, use a graphing utility to graph the regiondeterm...
 6.6.20: In Exercises 1720, use a graphing utility to graph the regiondeterm...
 6.6.21: In Exercises 2124, find the minimum and maximum valuesof the object...
 6.6.22: In Exercises 2124, find the minimum and maximum valuesof the object...
 6.6.23: In Exercises 2124, find the minimum and maximum valuesof the object...
 6.6.24: In Exercises 2124, find the minimum and maximum valuesof the object...
 6.6.25: In Exercises 2528, find the minimum and maximum values ofthe object...
 6.6.26: In Exercises 2528, find the minimum and maximum values ofthe object...
 6.6.27: In Exercises 2528, find the minimum and maximum values ofthe object...
 6.6.28: In Exercises 2528, find the minimum and maximum values ofthe object...
 6.6.29: In Exercises 2934, the linear programming problem has anunusual cha...
 6.6.30: In Exercises 2934, the linear programming problem has anunusual cha...
 6.6.31: In Exercises 2934, the linear programming problem has anunusual cha...
 6.6.32: In Exercises 2934, the linear programming problem has anunusual cha...
 6.6.33: In Exercises 2934, the linear programming problem has anunusual cha...
 6.6.34: In Exercises 2934, the linear programming problem has anunusual cha...
 6.6.35: OPTIMAL PROFIT A merchant plans to sell twomodels of MP3 players at...
 6.6.36: OPTIMAL PROFIT A manufacturer produces twomodels of elliptical cros...
 6.6.37: OPTIMAL COST An animal shelter mixes two brandsof dog food. Brand X...
 6.6.38: OPTIMAL COST A humanitarian agency can use twomodels of vehicles fo...
 6.6.39: OPTIMAL REVENUE An accounting firm has780 hours of staff time and 2...
 6.6.40: OPTIMAL REVENUE The accounting firm in Exercise 39lowers its charge...
 6.6.41: MEDIA SELECTION A company has budgeted amaximum of $1,000,000 for n...
 6.6.42: OPTIMAL COST According to AAA (AutomobileAssociation of America), o...
 6.6.43: INVESTMENT PORTFOLIO An investor has up to$250,000 to invest in two...
 6.6.44: INVESTMENT PORTFOLIO An investor has up to$450,000 to invest in two...
 6.6.45: TRUE OR FALSE? In Exercises 4547, determine whetherthe statement is...
 6.6.46: TRUE OR FALSE? In Exercises 4547, determine whetherthe statement is...
 6.6.47: TRUE OR FALSE? In Exercises 4547, determine whetherthe statement is...
 6.6.48: CAPSTONE Using the constraint region shownbelow, determine which of...
Solutions for Chapter 6.6: Linear Programming
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 6.6: Linear Programming
Get Full SolutionsChapter 6.6: Linear Programming includes 32 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Since 32 problems in chapter 6.6: Linear Programming have been answered, more than 33194 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9781439048696.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Solvable system Ax = b.
The right side b is in the column space of A.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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