EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 11, Problem 18P
An electronics company produces transistors, resistors, and computer chips. Each transistor requires four units of copper, one unit of zinc, and two units of glass. Each resistor requires three, three, and one units of the three materials, respectively, and each computer chip requires two, one, and three units of these materials, respectively. Putting this information into table form, we get:
| Component | Copper | Zinc | Glass |
| Transistors | 4 | 1 | 2 |
| Resistors | 3 | 3 | 1 |
| Computer chips | 2 | 1 | 3 |
Supplies of these materials vary from week to week, so the company needs to determine a different production run each week. For example, one week the total amounts of materials available are 960 units of copper, 510 units of zinc, and 610 units of glass. Set up the system of equations modeling the production run, and use Excel, MATLAB, or Mathcad, to solve for the number of transistors, resistors, and computer chips to be manufactured this week.
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Zaphod Beeblebrox is mixing drinks that contain three ingredients: Ol' Janx Spirit
(ingredient A), water from the seas of Santraginus V (ingredient B) and Arcturan
Mega-gin (ingredient C). On his shelf he has three mixtures M1, M2 and M3
containing ingredients A, B and C. The table below is showing the amounts in
decilitres of ingredients A, B and C that are contained in 11 of each of the mixtures
(11=10dcl).
M1 M2 M3
ingredient A
3
ingredient B
3
4
1
ingredient C
5
3
(a) Zaphod made a new mixture using 31 of M1, 21 of M2 and 11 of M3. Determine
the amount of each type of ingredient in this mixture.
(b) A recipe for Pan Galactic Gargle Blaster requires a mixture that contains 2dcl
of ingredient A, 3dcl of ingredient B and 5dcl of ingredient C. Zaphod wants
to prepare it using mixtures M1, M2 and M3. What is the minimal and what
is the maximal amount of mixture M3 that he can use?
Chapter 11 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 11 - 11.1 Perform the same calculations as in (a)...Ch. 11 - Determine the matrix inverse for Example 11.1...Ch. 11 - 11.3 The following tridiagonal system must be...Ch. 11 - 11.4 Confirm the validity of the Cholesky...Ch. 11 - Perform the same calculations as in Example 11.2,...Ch. 11 - Perform a Cholesky decomposition of the following...Ch. 11 - Compute the Cholesky decomposition of...Ch. 11 - Use the Gauss-Seidel method to solve the...Ch. 11 - Recall from Prob. 10.8, that the following system...Ch. 11 - 11.10 Repeat Prob. 11.9, but use Jacobi...
Ch. 11 - 11.11 Use the Gauss-Seidel method to solve the...Ch. 11 - Use the Gauss-Seidel method (a) without relaxation...Ch. 11 - 11.13 Use the Gauss-Seidel method (a) without...Ch. 11 - Redraw Fig. 11.5 for the case where the slopes of...Ch. 11 - 11.15 Of the following three sets of linear...Ch. 11 - Use the software package of your choice to obtain...Ch. 11 - Given the pair of nonlinear simultaneous...Ch. 11 - An electronics company produces transistors,...Ch. 11 - Use MATLAB or Mathcad software to determine the...Ch. 11 - Repeat Prob. 11.19. but for the case of a...Ch. 11 - 11.21 Given a square matrix , write a single line...Ch. 11 - Write the following set of equations in matrix...Ch. 11 - In Sec. 9.2.1, we determined the number of...Ch. 11 - 11.24 Develop a user-friendly program in either a...Ch. 11 - 11.25 Develop a user-friendly program in either a...Ch. 11 - Develop a user-friendly program in either a...Ch. 11 - As described in Sec. PT3.1.2, linear algebraic...Ch. 11 - A pentadiagonal system with a bandwidth of five...
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