 12.8.1: A linear programming problem requires that a linear expression, cal...
 12.8.2: True or False If a linear programming problem has a solution, it is...
 12.8.3: In 38, find the maximum and minimum value of the given objective fu...
 12.8.4: In 38, find the maximum and minimum value of the given objective fu...
 12.8.5: In 38, find the maximum and minimum value of the given objective fu...
 12.8.6: In 38, find the maximum and minimum value of the given objective fu...
 12.8.7: In 38, find the maximum and minimum value of the given objective fu...
 12.8.8: In 38, find the maximum and minimum value of the given objective fu...
 12.8.9: In 918,solve each linear programming problem.
 12.8.10: In 918,solve each linear programming problem.
 12.8.11: In 918,solve each linear programming problem.
 12.8.12: In 918,solve each linear programming problem.
 12.8.13: In 918,solve each linear programming problem.
 12.8.14: In 918,solve each linear programming problem.
 12.8.15: In 918,solve each linear programming problem.
 12.8.16: In 918,solve each linear programming problem.
 12.8.17: In 918,solve each linear programming problem.
 12.8.18: In 918,solve each linear programming problem.
 12.8.19: Maximizing Profit A manufacturer of skis produces two types: downhi...
 12.8.20: Farm Management A farmer has 70 acres of land available for plantin...
 12.8.21: Banquet Seating A banquet hall offers two types of tables for rent:...
 12.8.22: Spring Break The student activities department of a community colle...
 12.8.23: Return on Investment An investment broker is instructed by her clie...
 12.8.24: Production Scheduling In a factory, machine 1 produces 8inch (in.)...
 12.8.25: Managing a Meat Market A meat market combines ground beef and groun...
 12.8.26: Ice Cream The Mom and Pop Ice Cream Company makes two kinds of choc...
 12.8.27: Maximizing Profit on Ice Skates A factory manufactures two kinds of...
 12.8.28: Financial Planning A retired couple has up to $50,000 to place in f...
 12.8.29: Product Design An entrepreneur is having a design group produce at ...
 12.8.30: Animal Nutrition Kevins dog Amadeus likes two kinds of canned dog f...
 12.8.31: Airline Revenue An airline has two classes of service: first class ...
 12.8.32: Explain in your own words what a linear programming problem is and ...
Solutions for Chapter 12.8: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 12.8
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 32 problems in chapter 12.8 have been answered, more than 35388 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Chapter 12.8 includes 32 full stepbystep solutions.

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.

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.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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 matrix N.
The columns of N are the n  r special solutions to As = O.

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

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).