 5.1: In 18, determine which maximum problems are in standard form.P = 2x...
 5.2: In 18, determine which maximum problems are in standard form.P = x1...
 5.3: In 18, determine which maximum problems are in standard form.P = 5x...
 5.4: In 18, determine which maximum problems are in standard form.P = 2x...
 5.5: In 18, determine which maximum problems are in standard form.P = x1...
 5.6: In 18, determine which maximum problems are in standard form.P = 5x...
 5.7: In 18, determine which maximum problems are in standard form.P = x1...
 5.8: In 18, determine which maximum problems are in standard form.P = 4x...
 5.9: In 914, set up the initial tableau for each maximum problemP = 2x1 ...
 5.10: In 914, set up the initial tableau for each maximum problemP = x1 +...
 5.11: In 914, set up the initial tableau for each maximum problemP = 6x1 ...
 5.12: In 914, set up the initial tableau for each maximum problemP = 2x1 ...
 5.13: In 914, set up the initial tableau for each maximum problemP = x1 +...
 5.14: In 914, set up the initial tableau for each maximum problemP = x1 +...
 5.15: In 1522, use each tableau to: (a) Choose the pivot element and perf...
 5.16: In 1522, use each tableau to: (a) Choose the pivot element and perf...
 5.17: In 1522, use each tableau to: (a) Choose the pivot element and perf...
 5.18: In 1522, use each tableau to: (a) Choose the pivot element and perf...
 5.19: In 1522, use each tableau to: (a) Choose the pivot element and perf...
 5.20: In 1522, use each tableau to: (a) Choose the pivot element and perf...
 5.21: In 1522, use each tableau to: (a) Choose the pivot element and perf...
 5.22: In 1522, use each tableau to: (a) Choose the pivot element and perf...
 5.23: In 2326, use the simplex method to solve each maximum problem.P = 1...
 5.24: In 2326, use the simplex method to solve each maximum problem.P = x...
 5.25: In 2326, use the simplex method to solve each maximum problem.P = 4...
 5.26: In 2326, use the simplex method to solve each maximum problem.P = 2...
 5.27: In 2732, determine if the minimum problem is in standard form.C = 2...
 5.28: In 2732, determine if the minimum problem is in standard form.C = x...
 5.29: In 2732, determine if the minimum problem is in standard form.C = 2...
 5.30: In 2732, determine if the minimum problem is in standard form.C = x...
 5.31: In 2732, determine if the minimum problem is in standard form.C = x...
 5.32: In 2732, determine if the minimum problem is in standard form.C = 2...
 5.33: In 3336, write the dual of the minimum problem.C = 2x1 + x2
 5.34: In 3336, write the dual of the minimum problem.C = 4x1 + 2x2
 5.35: In 3336, write the dual of the minimum problem.C = 5x1 + 4x2 + 2x3
 5.36: In 3336, write the dual of the minimum problem.C = 2x1 + x2 + 3x3 + x4
 5.37: Solve using the duality principle.
 5.38: Solve using the duality principle.
 5.39: Solve using the duality principle.
 5.40: Solve using the duality principle.
 5.41: In 4146, solve each linear programming problem not in standard form...
 5.42: In 4146, solve each linear programming problem not in standard form...
 5.43: In 4146, solve each linear programming problem not in standard form...
 5.44: In 4146, solve each linear programming problem not in standard form...
 5.45: In 4146, solve each linear programming problem not in standard form...
 5.46: In 4146, solve each linear programming problem not in standard form...
 5.47: Maximizing Profit The finishing process in the manufacture of cockt...
 5.48: Management The manager of a supermarket meat department finds that ...
 5.49: Minimizing Cost The ACE Meat Market makes up a combination package ...
Solutions for Chapter 5: Linear Programming: Simplex Method
Full solutions for Finite Mathematics, Binder Ready Version: An Applied Approach  11th Edition
ISBN: 9780470876398
Solutions for Chapter 5: Linear Programming: Simplex Method
Get Full SolutionsSince 49 problems in chapter 5: Linear Programming: Simplex Method have been answered, more than 16708 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Finite Mathematics, Binder Ready Version: An Applied Approach, edition: 11. Finite Mathematics, Binder Ready Version: An Applied Approach was written by and is associated to the ISBN: 9780470876398. Chapter 5: Linear Programming: Simplex Method includes 49 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their 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.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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

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.

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

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).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

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.