Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts.
Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
6. Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts. Provide a dynamic programming approach to solve this problem given an initial rod of length n with potential cut lengths of 1, 2, 5, and 7 [Adapted from ITA, pg. 370, 15.1-3]
length of cut (i) 1 2 5 7
value (pi) 5 7 30 45
handling cost (ci) 4.5 6 10.5 13.5
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Algorithm:
MODIFIED-CUT-ROD(p,n,c)
let r[0..n] be a new array
r[0]=0
for j=1 to n
q=p[j]
for i=1 to j-1
q=max(q,p[i]+r[j-i]-c)
r[j]=q
return r[n]
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Database System Concepts](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
![Starting Out with Python (4th Edition)](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
![Digital Fundamentals (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
![Database System Concepts](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
![Starting Out with Python (4th Edition)](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
![Digital Fundamentals (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
![C How to Program (8th Edition)](https://www.bartleby.com/isbn_cover_images/9780133976892/9780133976892_smallCoverImage.gif)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
![Database Systems: Design, Implementation, & Manag…](https://www.bartleby.com/isbn_cover_images/9781337627900/9781337627900_smallCoverImage.gif)
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education