Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 11.0A, Problem 30E
To determine
(a)
To find:
The product AB of the matrices if it exists.
To determine
(b)
To find:
The product BA of the matrices if it exists.
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Suppose we have a linear program in standard equation form
maximize c'x
subject to Ax=b,
x≥ 0.
and suppose u, v, and w are all optimal solutions to this linear program.
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(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
(a) For the following linear programme, sketch the feasible region and the direction
of the objective function. Use you sketch to find an optimal solution to the
program. State the optimal solution and give the objective value for this
solution.
maximize +22
subject to 1 + 2x2 ≤ 4,
1 +3x2 ≤ 12,
x1, x2 ≥0
(b) For the following linear programme, sketch the feasible region and the direction
of the objective function. Explain, making reference to your sketch, why this
linear programme is unbounded.
maximize
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subject to
-2x1 + x2 ≤ 4,
x1 - 2x2 ≤4,
x1 + x2 ≥ 7,
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Give any feasible solution to the linear programme for which the objective
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find the domain of the function f(x)
Chapter 11 Solutions
Mathematics: A Practical Odyssey
Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...Ch. 11.0A - Prob. 2ECh. 11.0A - Prob. 3ECh. 11.0A - Prob. 4ECh. 11.0A - Prob. 5ECh. 11.0A - Prob. 6ECh. 11.0A - Prob. 7ECh. 11.0A - Prob. 8ECh. 11.0A - Prob. 9ECh. 11.0A - In Exercises 1-10, a find the dimensions of the...
Ch. 11.0A - Prob. 11ECh. 11.0A - Prob. 12ECh. 11.0A - Prob. 13ECh. 11.0A - Prob. 14ECh. 11.0A - Prob. 15ECh. 11.0A - Prob. 16ECh. 11.0A - Prob. 17ECh. 11.0A - Prob. 18ECh. 11.0A - Prob. 19ECh. 11.0A - Prob. 20ECh. 11.0A - Prob. 21ECh. 11.0A - Prob. 22ECh. 11.0A - Prob. 23ECh. 11.0A - Prob. 24ECh. 11.0A - Prob. 25ECh. 11.0A - Prob. 26ECh. 11.0A - Prob. 27ECh. 11.0A - Prob. 28ECh. 11.0A - Prob. 29ECh. 11.0A - Prob. 30ECh. 11.0A - Prob. 31ECh. 11.0A - Prob. 32ECh. 11.0A - Prob. 33ECh. 11.0A - Prob. 34ECh. 11.0A - Prob. 35ECh. 11.0A - Prob. 36ECh. 11.0A - Prob. 37ECh. 11.0A - Prob. 38ECh. 11.0A - Prob. 39ECh. 11.0A - Prob. 40ECh. 11.0A - Prob. 41ECh. 11.0A - Prob. 42ECh. 11.0A - Prob. 43ECh. 11.0A - Prob. 44ECh. 11.0A - Prob. 45ECh. 11.0A - Prob. 46ECh. 11.0A - Prob. 47ECh. 11.0A - Prob. 48ECh. 11.0A - Prob. 49ECh. 11.0A - Prob. 50ECh. 11.0A - Prob. 51ECh. 11.0A - Prob. 52ECh. 11.0A - Prob. 53ECh. 11.0A - Prob. 54ECh. 11.0A - Prob. 55ECh. 11.0A - Prob. 56ECh. 11.0A - Prob. 57ECh. 11.0A - Prob. 58ECh. 11.0A - Prob. 59ECh. 11.0A - Prob. 60ECh. 11.0A - Prob. 61ECh. 11.0A - Prob. 62ECh. 11.0B - Prob. 1ECh. 11.0B - Prob. 2ECh. 11.0B - Prob. 3ECh. 11.0B - Prob. 4ECh. 11.0B - Prob. 5ECh. 11.0B - Prob. 6ECh. 11.0B - Prob. 7ECh. 11.0B - Prob. 8ECh. 11.0B - Prob. 9ECh. 11.0B - Prob. 10ECh. 11.0B - Prob. 11ECh. 11.0B - Prob. 12ECh. 11.0B - Prob. 13ECh. 11.0B - Prob. 14ECh. 11.0B - Prob. 15ECh. 11.0B - Prob. 16ECh. 11.0B - Prob. 17ECh. 11.0B - Prob. 18ECh. 11.0B - Prob. 19ECh. 11.0B - Prob. 20ECh. 11.0B - Prob. 21ECh. 11.0B - Prob. 22ECh. 11.0B - Prob. 23ECh. 11.0B - Prob. 24ECh. 11.0B - Prob. 25ECh. 11.0B - Prob. 26ECh. 11.0B - Prob. 27ECh. 11.0B - Prob. 28ECh. 11.0B - Prob. 29ECh. 11.0B - Prob. 30ECh. 11.0B - Prob. 31ECh. 11.0B - Prob. 32ECh. 11.0B - Prob. 33ECh. 11.0B - Prob. 34ECh. 11.0B - Prob. 35ECh. 11.0B - Prob. 36ECh. 11.0B - Why could you not use a graphing calculator to...Ch. 11.1 - Prob. 1ECh. 11.1 - In Exercises 1-4, a write the given data in...Ch. 11.1 - Prob. 3ECh. 11.1 - In Exercises 1-4, a write the given data in...Ch. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Use the information in Exercise 3 to predict the...Ch. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10ECh. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - In Exercises 511, round all percents to the...Ch. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - In Exercises 5-11, round all percent to the...Ch. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Monopoly is the most played board game in the...Ch. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.5 - Prob. 1ECh. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Prob. 5ECh. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.CR - Prob. 1CRCh. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Prob. 20CRCh. 11.CR - Prob. 21CRCh. 11.CR - Prob. 22CRCh. 11.CR - Prob. 23CRCh. 11.CR - Prob. 24CRCh. 11.CR - Prob. 25CRCh. 11.CR - Prob. 26CRCh. 11.CR - Prob. 27CRCh. 11.CR - Prob. 28CRCh. 11.CR - Prob. 29CRCh. 11.CR - Prob. 30CRCh. 11.CR - Prob. 31CRCh. 11.CR - Prob. 32CRCh. 11.CR - Prob. 33CR
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