Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 16, Problem 31P
A manufacturing firm produces four types of automobile parts. Each is first fabricated and then finished. The required worker hours and profit for each part are
| Part | ||||
| A | B | C | D | |
| Fabrication time (hr/100 units) | 2.5 | 1.5 | 2.75 | 2 |
| Finishing time (hr/100 units) | 3.5 | 3 | 3 | 2 |
| Profit ($/100 units) | 375 | 275 | 475 | 324 |
The capacities of the fabrication and finishing shops over the next month are 640 and 960 hours, respectively. Determine how many of each part should be produced in order to maximize profit.
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Topic: Group Theory | Abstract Algebra
Question:
Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe
the number of Sylow subgroups for each.
Instructions:
•
Use Sylow's Theorems (existence, conjugacy, and counting).
•
List divisors of 45 and compute possibilities for n for p = 3 and p = 5.
Show that if n = 1, the subgroup is normal.
Conclude about group structure using your analysis.
Topic: Group Theory | Abstract Algebra
Question:
Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe
the number of Sylow subgroups for each.
Instructions:
•
Use Sylow's Theorems (existence, conjugacy, and counting).
•
List divisors of 45 and compute possibilities for n for p = 3 and p = 5.
Show that if n = 1, the subgroup is normal.
Conclude about group structure using your analysis.
Topic: Group Theory | Abstract Algebra
Question:
Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe
the number of Sylow subgroups for each.
Instructions:
•
Use Sylow's Theorems (existence, conjugacy, and counting).
•
List divisors of 45 and compute possibilities for n for p = 3 and p = 5.
Show that if n = 1, the subgroup is normal.
Conclude about group structure using your analysis.
Chapter 16 Solutions
Numerical Methods for Engineers
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