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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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
Resistors
3
Computer chips
2
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.
(a)Set up the system of equations modeling the production run.
(b)Test for the diagonal dominance for the convergence criteria.
(c)Use appropriate method based on the convergence criteria to solve for the number of transistors, resistors, and computer chips to be…
Please read the problem carefully. Thank you!
An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units
of copper, 1 unit of zinc, and 2 units of glass. Each resistor requires 3, 2, and 1 units of the three materials, and each
computer chip requires 2, 1, and 2 units of these materials, respectively. How many of each product can be made with
the following amounts of materials? Complete parts (a) through (c) below.
(a) Let x represent the number of transistors that can be made, y the number of resistors, and z the number of
computer chips. Write a system of three linear equations when the amounts of available materials are 810 units
of copper, 420 units of zinc, and 480 units of glass. Choose the correct answer below.
A. 3x+3y + 2z = 810
x+2y+z= 420
2x+y + 2z = 480
C. x+3y + 2z = 480
3x + 3y + 2z = 420
x+2y+z=810
The company can make
transistors, resistors, and
O B. x+y+z= 420
2x+y+z=810
2x+y + 2z=480
O D. 3x + 3y + 2z = 420
x+2y+z=810
2x+y + 2z = 480
computer chips.
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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