Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Chapter 3.1, Problem 9ES
To determine
To find: The value of y by using the given data.
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Students have asked these similar questions
Suppose we have a linear program in standard equation form
maximize cTx
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) 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
x2 x3
81 82
83
84
81
-2 0
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
Microsoft Excel snapshot for random sampling: Also note the formula used for the last
column
02
x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
A
B
1
No.
States
2
1
ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
B
E
F
G
1
No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
sample
10
3
2 ALASKA
0.4493186 OKLAHOMA
k
5
4
3 ARIZONA
0.707914 KANSAS
5
4 ARKANSAS 0.4831379 NORTH DAKOTA
6
5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
9
8 DELAWARE 0.5783029 MISSOURI
525
10
15
INDIANA
MARYLAND
COLORADO
Chapter 3 Solutions
Numerical Analysis
Ch. 3.1 - For the given functions f(x), let x0 = 0, x1 =...Ch. 3.1 - Use Theorem 3.3 to find an error bound for the...Ch. 3.1 - Prob. 4ESCh. 3.1 - The data for Exercise 6 were generated using the...Ch. 3.1 - Prob. 9ESCh. 3.1 - Prob. 10ESCh. 3.1 - Prob. 11ESCh. 3.1 - Prob. 12ESCh. 3.1 - Prob. 15ESCh. 3.1 - Prob. 17ES
Ch. 3.1 - It is suspected that the high amounts of tannin in...Ch. 3.1 - Prob. 21ESCh. 3.1 - Prove Taylors Theorem 1.14 by following the...Ch. 3.1 - Prob. 1DQCh. 3.1 - If we decide to increase the degree of the...Ch. 3.2 - Let P3(x) be the interpolating polynomial for the...Ch. 3.2 - Nevilles method is used to approximate f(0.4),...Ch. 3.2 - Nevilles method is used to approximate f(0.5),...Ch. 3.2 - Suppose xj = j, for j = 0, 1, 2, 3, and it is...Ch. 3.2 - Nevilles Algorithm is used to approximate f(0)...Ch. 3.2 - Prob. 11ESCh. 3.2 - Prob. 13ESCh. 3.2 - Can Nevilles method be used to obtain the...Ch. 3.3 - Use Eq. (3.10) or Algorithm 3.2 to construct...Ch. 3.3 - Use Eq. (3.10) or Algorithm 3.2 to construct...Ch. 3.3 - Use the Newton forward-difference formula to...Ch. 3.3 - Use the Newton forward-difference formula to...Ch. 3.3 - Use the Newton backward-difference formula to...Ch. 3.3 - Use the Newton backward-difference formula to...Ch. 3.3 - a. Use Algorithm 3.2 to construct the...Ch. 3.3 - a. Use Algorithm 3.2 to construct the...Ch. 3.3 - a. Approximate f(0.05) using the following data...Ch. 3.3 - The following data are given for a polynomial P(x)...Ch. 3.3 - The following data are given for a polynomial P(x)...Ch. 3.3 - The Newton forward-difference formula is used to...Ch. 3.3 - Prob. 14ESCh. 3.3 - Prob. 16ESCh. 3.3 - Prob. 17ESCh. 3.3 - Show that the polynomial interpolating the...Ch. 3.3 - Prob. 20ESCh. 3.3 - Prob. 21ESCh. 3.3 - Prob. 22ESCh. 3.3 - Prob. 23ESCh. 3.3 - Compare and contrast the various...Ch. 3.3 - Is it easier to add a new data pair using...Ch. 3.3 - Prob. 3DQCh. 3.4 - Use Theorem 3.9 or Algorithm 3.3 to construct an...Ch. 3.4 - Use Theorem 3.9 or Algorithm 3.3 to construct an...Ch. 3.4 - The data in Exercise 1 were generated using the...Ch. 3.4 - The data in Exercise 2 were generated using the...Ch. 3.4 - Let f (x) = 3xex e2x. a. Approximate f (1.03) by...Ch. 3.4 - The following table lists data for the function...Ch. 3.4 - a. Show that H2n + 1 (x) is the unique polynomial...Ch. 3.4 - Prob. 1DQCh. 3.4 - Prob. 2DQCh. 3.4 - Prob. 3DQCh. 3.5 - Determine the natural cubic spline S that...Ch. 3.5 - Determine the clamped cubic spline s that...Ch. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - The data in Exercise 3 were generated using the...Ch. 3.5 - Prob. 6ESCh. 3.5 - Prob. 8ESCh. 3.5 - Prob. 11ESCh. 3.5 - Prob. 12ESCh. 3.5 - Prob. 13ESCh. 3.5 - Prob. 14ESCh. 3.5 - Given the partition x0 = 0, x1 = 0.05, and x2 =...Ch. 3.5 - Prob. 16ESCh. 3.5 - Prob. 21ESCh. 3.5 - Prob. 22ESCh. 3.5 - Prob. 23ESCh. 3.5 - It is suspected that the high amounts of tannin in...Ch. 3.5 - Prob. 29ESCh. 3.5 - Prob. 30ESCh. 3.5 - Prob. 31ESCh. 3.5 - Prob. 32ESCh. 3.5 - Let f C2[a, b] and let the nodes a = x0 x1 xn...Ch. 3.5 - Prob. 34ESCh. 3.5 - Prob. 35ESCh. 3.6 - Let (x0, y0) = (0,0) and (x1, y1) = (5, 2) be the...Ch. 3.6 - Prob. 2ESCh. 3.6 - Prob. 5ESCh. 3.6 - Prob. 1DQ
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