ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE
10th Edition
ISBN: 9781119809210
Author: Kreyszig
Publisher: WILEY
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Chapter 1.6, Problem 2P
To determine
To represent: The family of circles with center on the cubic parabola
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You manage a chemical company with 2 warehouses. The following quantities of
Important Chemical A have arrived from an international supplier at 3 different
ports:
Chemical Available (L)
Port 1
Port 2
Port 3
400
110
100
The following amounts of Important Chemical A are required at your warehouses:
Warehouse 1
Warehouse 2
Chemical Required (L)
380
230
The cost in £ to ship 1L of chemical from each port to each warehouse is as follows:
Warehouse 1 Warehouse 2
Port 1
£10
£45
Port 2
£20
£28
Port 3
£13
£11
(a) You want to know how to send these shipments as cheaply as possible. For-
mulate this as a linear program (you do not need to formulate it in standard
inequality form) indicating what each variable represents.
a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1 12 23
81
82
83
S4
$1
-20
1 1
0
0
0
3
82
3 0
-2
0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0
-1 1 4
2
-2
0 11
0
0
-4
0
-8
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the initial tableau and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize 21 - - 2x2 + x3 - 4x4
subject to 2x1+x22x3x4≥ 1,
5x1+x2-x3-4 -1,
2x1+x2-x3-342,
1, 2, 3, 4 ≥0.
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.
Chapter 1 Solutions
ADV.ENG.MATH (LL) W/WILEYPLUS BUNDLE
Ch. 1.1 - Prob. 1PCh. 1.1 - Prob. 2PCh. 1.1 - Prob. 3PCh. 1.1 - Prob. 4PCh. 1.1 - Prob. 5PCh. 1.1 - Prob. 6PCh. 1.1 - Prob. 7PCh. 1.1 - Prob. 8PCh. 1.1 - Prob. 9PCh. 1.1 - Prob. 10P
Ch. 1.1 - Prob. 11PCh. 1.1 - Prob. 12PCh. 1.1 - Prob. 13PCh. 1.1 - Prob. 14PCh. 1.1 - 9–15 VERIFICATION. INITIAL VALUE PROBLEM...Ch. 1.1 - Prob. 16PCh. 1.1 - Half-life. The half-life measures exponential...Ch. 1.1 - Half-life. Radium has a half-life of about 3.6...Ch. 1.1 - Prob. 19PCh. 1.1 - Exponential decay. Subsonic flight. The efficiency...Ch. 1.2 - DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - 1–8 DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - Prob. 4PCh. 1.2 - DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - Prob. 6PCh. 1.2 - DIRECTION FIELDS, SOLUTION CURVES
Graph a...Ch. 1.2 - Prob. 8PCh. 1.2 - Prob. 9PCh. 1.2 - Prob. 10PCh. 1.2 - Autonomous ODE. This means an ODE not showing x...Ch. 1.2 - Model the motion of a body B on a straight line...Ch. 1.2 - Prob. 13PCh. 1.2 - Prob. 14PCh. 1.2 - Prob. 15PCh. 1.2 - Prob. 16PCh. 1.2 - EULER’S METHOD
This is the simplest method to...Ch. 1.2 - EULER’S METHOD
This is the simplest method to...Ch. 1.2 - EULER’S METHOD
This is the simplest method to...Ch. 1.2 - EULER’S METHOD
This is the simplest method to...Ch. 1.3 - Prob. 1PCh. 1.3 - Prob. 2PCh. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - GENERAL SOLUTION
Find a general solution. Show the...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - Prob. 17PCh. 1.3 - Prob. 18PCh. 1.3 - INITIAL VALUE PROBLEMS (IVPs)
Solve the IVP. Show...Ch. 1.3 - Prob. 20PCh. 1.3 - Radiocarbon dating. What should be the content...Ch. 1.3 - Prob. 22PCh. 1.3 - Prob. 23PCh. 1.3 - Prob. 24PCh. 1.3 - Prob. 25PCh. 1.3 - Prob. 26PCh. 1.3 - Prob. 27PCh. 1.3 - Prob. 28PCh. 1.3 - Prob. 29PCh. 1.3 - Prob. 30PCh. 1.3 - Prob. 31PCh. 1.3 - Prob. 32PCh. 1.3 - Prob. 33PCh. 1.3 - Prob. 36PCh. 1.4 - Prob. 1PCh. 1.4 - Prob. 2PCh. 1.4 - Prob. 3PCh. 1.4 - Prob. 4PCh. 1.4 - Prob. 5PCh. 1.4 - Prob. 6PCh. 1.4 - Prob. 7PCh. 1.4 - Prob. 8PCh. 1.4 - Prob. 9PCh. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - ODEs. INTEGRATING FACTORS
Test for exactness. If...Ch. 1.4 - Exactness. Under what conditions for the constants...Ch. 1.4 - Prob. 17PCh. 1.4 - Prob. 18PCh. 1.5 - CAUTION! Show that e−ln x = 1/x (not −x) and...Ch. 1.5 - Prob. 2PCh. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
Find the...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
7. xy′ =...Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
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9.
Ch. 1.5 - GENERAL SOLUTION. INITIAL VALUE PROBLEMS
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These properties...Ch. 1.5 - Prob. 21PCh. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - NONLINEAR ODEs
Using a method of this section or...Ch. 1.5 - Prob. 29PCh. 1.5 - MODELING. FURTHER APPLICATIONS
31. Newton’s law of...Ch. 1.5 - Prob. 32PCh. 1.5 - MODELING. FURTHER APPLICATIONS
33. Drug injection....Ch. 1.5 - MODELING. FURTHER APPLICATIONS
34. Epidemics. A...Ch. 1.5 - MODELING. FURTHER APPLICATIONS
35. Lake Erie. Lake...Ch. 1.5 - MODELING. FURTHER APPLICATIONS
36. Harvesting...Ch. 1.5 - Prob. 37PCh. 1.5 - Prob. 38PCh. 1.5 - Prob. 39PCh. 1.5 - Prob. 40PCh. 1.6 -
Represent the given family of curves in the form...Ch. 1.6 - Prob. 2PCh. 1.6 -
Represent the given family of curves in the form...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - ORTHOGONAL TRAJECTORIES (OTs)
Sketch or graph some...Ch. 1.6 - APPLICATIONS, EXTENSIONS
11. Electric field. Let...Ch. 1.6 - Electric field. The lines of electric force of two...Ch. 1.6 - Prob. 13PCh. 1.6 - Conic sections. Find the conditions under which...Ch. 1.6 - Prob. 15PCh. 1.6 - Prob. 16PCh. 1.7 - Prob. 1PCh. 1.7 - Existence? Does the initial value problem (x −...Ch. 1.7 - Vertical strip. If the assumptions of Theorems 1...Ch. 1.7 - Change of initial condition. What happens in Prob....Ch. 1.7 - Prob. 5PCh. 1.7 - Maximum α. What is the largest possible α in...Ch. 1.7 - Prob. 8PCh. 1.7 - Common points. Can two solution curves of the same...Ch. 1.7 - Three possible cases. Find all initial conditions...Ch. 1 - Prob. 1RQCh. 1 - Prob. 2RQCh. 1 - Does every first-order ODE have a solution? A...Ch. 1 - What is a direction field? A numeric method for...Ch. 1 - What is an exact ODE? Is f(x) dx + g(y) dy = 0...Ch. 1 - Prob. 6RQCh. 1 - What other solution methods did we consider in...Ch. 1 - Can an ODE sometimes be solved by several methods?...Ch. 1 - Prob. 9RQCh. 1 - Prob. 10RQCh. 1 - Prob. 11RQCh. 1 - Prob. 12RQCh. 1 - Prob. 13RQCh. 1 - Prob. 14RQCh. 1 - Prob. 15RQCh. 1 - DIRECTION FIELD: NUMERIC SOLUTION
Graph a...Ch. 1 - Prob. 17RQCh. 1 - Prob. 18RQCh. 1 - Prob. 19RQCh. 1 - Prob. 20RQCh. 1 - Prob. 21RQCh. 1 - Prob. 22RQCh. 1 - Prob. 23RQCh. 1 - Prob. 24RQCh. 1 - Prob. 25RQCh. 1 - Prob. 26RQCh. 1 - Prob. 27RQCh. 1 - Prob. 28RQCh. 1 - Half-life. If in a reactor, uranium loses 10% of...Ch. 1 - Prob. 30RQ
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