ADVANCED ENGINEERING MATHEMATICS
10th Edition
ISBN: 9781119664697
Author: Kreyszig
Publisher: WILEY
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Question
Chapter 9.1, Problem 4P
To determine
The components of the
To determine
The value of
To determine
The unit vector
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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.
(a) Prove that zu+v+w is an optimal solution.
(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
₁+%2
subject to
-2x1 + x2 ≤ 4,
x1 - 2x2 ≤4,
x1 + x2 ≥ 7,
x1,x20
Give any feasible solution to the linear programme for which the objective
value is 40 (you do not need to justify your answer).
find the domain of the function f(x)
Chapter 9 Solutions
ADVANCED ENGINEERING MATHEMATICS
Ch. 9.1 - Prob. 1PCh. 9.1 - Find the components of the vector v with initial...Ch. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Find the components of the vector v with initial...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...
Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 13PCh. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 17PCh. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - What laws do Probs. 12–16 illustrate?
12. (a + b)...Ch. 9.1 - Prob. 20PCh. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Prob. 22PCh. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Equilibrium. Find v such that p, q, u in Prob. 21...Ch. 9.1 - Find p such that u, v, w in Prob. 23 and p are in...Ch. 9.1 - Unit vector. Find the unit vector in the direction...Ch. 9.1 - Restricted resultant. Find all v such that the...Ch. 9.1 - Prob. 30PCh. 9.1 - For what k is the resultant of [2, 0, −7], [1, 2,...Ch. 9.1 - If |p| = 6 and |q| = 4, what can you say about the...Ch. 9.1 - Same question as in Prob. 32 if |p| = 9, |q| = 6,...Ch. 9.1 - Relative velocity. If airplanes A and B are moving...Ch. 9.1 - Same question as in Prob. 34 for two ships moving...Ch. 9.1 - Prob. 36PCh. 9.1 - Prob. 37PCh. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 8PCh. 9.2 - Prob. 9PCh. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 11PCh. 9.2 - What does u • v = u • w imply if u = 0? If u ≠...Ch. 9.2 - Prove the Cauchy–Schwarz inequality.
Ch. 9.2 - Verify the Cauchy–Schwarz and triangle...Ch. 9.2 - Prob. 15PCh. 9.2 - Triangle inequality. Prove Eq. (7). Hint. Use Eq....Ch. 9.2 - Prob. 17PCh. 9.2 - Prob. 18PCh. 9.2 - Prob. 19PCh. 9.2 - Prob. 20PCh. 9.2 - Prob. 21PCh. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - What will happen to the angle in Prob. 24 if we...Ch. 9.2 - Prob. 26PCh. 9.2 - Addition law. cos (α − β) = cos α cos β + sin α...Ch. 9.2 - Prob. 28PCh. 9.2 - Prob. 29PCh. 9.2 - Prob. 30PCh. 9.2 - Prob. 31PCh. 9.2 - Prob. 32PCh. 9.2 - Prob. 33PCh. 9.2 - Prob. 34PCh. 9.2 - Prob. 35PCh. 9.2 - Prob. 36PCh. 9.2 - Prob. 37PCh. 9.2 - Prob. 38PCh. 9.2 - Prob. 39PCh. 9.2 - Prob. 40PCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.3 - Prob. 8PCh. 9.3 - Prob. 9PCh. 9.3 - Prob. 11PCh. 9.3 - Prob. 12PCh. 9.3 - Prob. 13PCh. 9.3 - Prob. 14PCh. 9.3 - Prob. 15PCh. 9.3 - Prob. 16PCh. 9.3 - Prob. 17PCh. 9.3 - Prob. 18PCh. 9.3 - Prob. 19PCh. 9.3 - Prob. 20PCh. 9.3 - Prob. 21PCh. 9.3 - Prob. 22PCh. 9.3 - Prob. 23PCh. 9.3 - Prob. 25PCh. 9.3 - Prob. 26PCh. 9.3 - Prob. 27PCh. 9.3 - Prob. 28PCh. 9.3 - Prob. 29PCh. 9.3 - Prob. 30PCh. 9.3 - Prob. 31PCh. 9.3 - Prob. 32PCh. 9.3 - Prob. 33PCh. 9.3 - Prob. 34PCh. 9.4 - Prob. 1PCh. 9.4 - Prob. 2PCh. 9.4 - Prob. 3PCh. 9.4 - Prob. 4PCh. 9.4 - Prob. 5PCh. 9.4 - Prob. 6PCh. 9.4 - Prob. 7PCh. 9.4 - Prob. 9PCh. 9.4 - Prob. 10PCh. 9.4 - Prob. 11PCh. 9.4 - Prob. 12PCh. 9.4 - Prob. 13PCh. 9.4 - Prob. 14PCh. 9.4 - Prob. 15PCh. 9.4 - Prob. 16PCh. 9.4 - Prob. 17PCh. 9.4 - Prob. 18PCh. 9.4 - Prob. 19PCh. 9.4 - Prob. 20PCh. 9.4 - Prob. 22PCh. 9.4 - Prob. 23PCh. 9.4 - Prob. 24PCh. 9.5 - Prob. 1PCh. 9.5 - Prob. 2PCh. 9.5 - Prob. 3PCh. 9.5 - Prob. 4PCh. 9.5 - Prob. 5PCh. 9.5 - Prob. 6PCh. 9.5 - Prob. 7PCh. 9.5 - Prob. 8PCh. 9.5 - Prob. 9PCh. 9.5 - Prob. 10PCh. 9.5 - Prob. 11PCh. 9.5 - Prob. 12PCh. 9.5 - Prob. 13PCh. 9.5 - Prob. 14PCh. 9.5 - Prob. 15PCh. 9.5 - Prob. 16PCh. 9.5 - Prob. 17PCh. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 20PCh. 9.5 - Prob. 21PCh. 9.5 - r(t) = [10 cos t, 1, 10 sin t], P: (6, 1, 8)Ch. 9.5 - r(t) = [cos t, sin t, 9t], P: (1, 0, 18)Ch. 9.5 - Prob. 27PCh. 9.5 - Prob. 29PCh. 9.5 - Prob. 30PCh. 9.5 - Prob. 31PCh. 9.5 - Prob. 32PCh. 9.5 - Prob. 33PCh. 9.5 - Prob. 34PCh. 9.5 - Prob. 35PCh. 9.5 - Prob. 36PCh. 9.5 - Prob. 37PCh. 9.5 - Prob. 38PCh. 9.5 - Prob. 43PCh. 9.5 - Prob. 44PCh. 9.5 - Prob. 45PCh. 9.5 - Prob. 46PCh. 9.5 - CURVATURE AND TORSION
47. Circle. Show that a...Ch. 9.5 - Prob. 48PCh. 9.5 - Prob. 49PCh. 9.5 - Prob. 50PCh. 9.5 - Prob. 51PCh. 9.5 - Prob. 52PCh. 9.5 - Prob. 53PCh. 9.5 - Prob. 54PCh. 9.5 - Prob. 55PCh. 9.7 - Prob. 1PCh. 9.7 - Prob. 2PCh. 9.7 - Prob. 3PCh. 9.7 - Prob. 4PCh. 9.7 - Prob. 5PCh. 9.7 - Prob. 6PCh. 9.7 - Prob. 7PCh. 9.7 - Prob. 8PCh. 9.7 - Prob. 9PCh. 9.7 - Prob. 10PCh. 9.7 - Prob. 11PCh. 9.7 - Prob. 12PCh. 9.7 - Prob. 13PCh. 9.7 - Prob. 14PCh. 9.7 - Prob. 15PCh. 9.7 - Prob. 16PCh. 9.7 - Prob. 17PCh. 9.7 - Prob. 18PCh. 9.7 - Prob. 19PCh. 9.7 - Prob. 20PCh. 9.7 - Prob. 21PCh. 9.7 - Prob. 22PCh. 9.7 - Prob. 23PCh. 9.7 - Prob. 24PCh. 9.7 - Prob. 25PCh. 9.7 - Prob. 26PCh. 9.7 - Prob. 28PCh. 9.7 - Prob. 29PCh. 9.8 - Prob. 1PCh. 9.8 - Prob. 2PCh. 9.8 - Prob. 3PCh. 9.8 - Prob. 4PCh. 9.8 - Prob. 5PCh. 9.8 - Prob. 6PCh. 9.8 - Prob. 7PCh. 9.8 - Prob. 8PCh. 9.8 - CAS EXPERIMENT. Visualizing the Divergence. Graph...Ch. 9.8 - Prob. 11PCh. 9.8 - Prob. 12PCh. 9.8 - Prob. 13PCh. 9.8 - Prob. 14PCh. 9.8 - Prob. 15PCh. 9.8 - Prob. 16PCh. 9.8 - Prob. 17PCh. 9.8 - Prob. 18PCh. 9.8 - Prob. 19PCh. 9.8 - Prob. 20PCh. 9.9 - Prob. 1PCh. 9.9 - Prob. 2PCh. 9.9 - Prob. 3PCh. 9.9 - Prob. 4PCh. 9.9 - Prob. 5PCh. 9.9 - Prob. 6PCh. 9.9 - Prob. 7PCh. 9.9 - Prob. 8PCh. 9.9 - Prob. 9PCh. 9.9 - Prob. 10PCh. 9.9 - Prob. 11PCh. 9.9 - Prob. 12PCh. 9.9 - Prob. 13PCh. 9.9 - Prob. 15PCh. 9.9 - Prob. 16PCh. 9.9 - Prob. 17PCh. 9.9 - Prob. 18PCh. 9.9 - Prob. 19PCh. 9.9 - Prob. 20PCh. 9 - Prob. 1RQCh. 9 - Prob. 2RQCh. 9 - Prob. 3RQCh. 9 - Prob. 4RQCh. 9 - Prob. 5RQCh. 9 - Prob. 6RQCh. 9 - Prob. 7RQCh. 9 - Prob. 8RQCh. 9 - Prob. 9RQCh. 9 - Prob. 11RQCh. 9 - Prob. 12RQCh. 9 - Prob. 13RQCh. 9 - Prob. 14RQCh. 9 - Prob. 15RQCh. 9 - Prob. 16RQCh. 9 - Prob. 17RQCh. 9 - Prob. 18RQCh. 9 - Prob. 19RQCh. 9 - Prob. 20RQCh. 9 - Prob. 21RQCh. 9 - Prob. 22RQCh. 9 - Prob. 23RQCh. 9 - Prob. 24RQCh. 9 - Prob. 25RQCh. 9 - Prob. 26RQCh. 9 - Prob. 27RQCh. 9 - Prob. 28RQCh. 9 - Prob. 29RQCh. 9 - Prob. 30RQCh. 9 - Prob. 31RQCh. 9 - Prob. 32RQCh. 9 - Prob. 33RQCh. 9 - Prob. 34RQCh. 9 - Prob. 35RQCh. 9 - Prob. 36RQCh. 9 - Prob. 37RQCh. 9 - Prob. 38RQCh. 9 - Prob. 39RQCh. 9 - Prob. 40RQ
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