The formulation of the problem is as follows: Given a rod of length n inches and...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The formulation of the problem is as follows: Given a rod of length n inches and a table of prices p, for i = 1, 2, ...,n, determine the maximum revenue r obtainable by cutting up the rod and selling the pieces. Note that if the price pn for a rod of length n is large enough, an optimal solution may require no cutting at all. a) Formulate this problem using sub problems. b) Analyse the sub-problems and comment on whether the sub-sub-problems of those sub-problems overlap or not. 10 length, i1 2 3 4 5 6 7 8 9 price, p 1 5 8 10 14 8 9 7 4 13 Table 1: Length and associated price for an instance of a rod cutting problem c) For the instance of the rod-cutting problem given in Table 1, can you find an optimal solution? Build a dynamic-programming table and analyse that table to find the optimal solution. You can write necessary code to build the table. Include the table in your report. d) Does the following "greedy" strategy work for the instance of the rod-cutting problem given in Table 1? Define the density of a rod of length i to be p/i, that is, its value per inch. The greedy strategy ctivate Win for a rod of length n cuts off a first piece of length i, where 1 i n, having maximum density. Go to Settings to It then continues by applying the greedy strategy to the remaining piece of length n - i. The formulation of the problem is as follows: Given a rod of length n inches and a table of prices p, for i = 1, 2, ...,n, determine the maximum revenue r obtainable by cutting up the rod and selling the pieces. Note that if the price pn for a rod of length n is large enough, an optimal solution may require no cutting at all. a) Formulate this problem using sub problems. b) Analyse the sub-problems and comment on whether the sub-sub-problems of those sub-problems overlap or not. 10 length, i1 2 3 4 5 6 7 8 9 price, p 1 5 8 10 14 8 9 7 4 13 Table 1: Length and associated price for an instance of a rod cutting problem c) For the instance of the rod-cutting problem given in Table 1, can you find an optimal solution? Build a dynamic-programming table and analyse that table to find the optimal solution. You can write necessary code to build the table. Include the table in your report. d) Does the following "greedy" strategy work for the instance of the rod-cutting problem given in Table 1? Define the density of a rod of length i to be p/i, that is, its value per inch. The greedy strategy ctivate Win for a rod of length n cuts off a first piece of length i, where 1 i n, having maximum density. Go to Settings to It then continues by applying the greedy strategy to the remaining piece of length n - i.
Expert Answer:
Answer rating: 100% (QA)
a Formulation using Subproblems The rodcutting problem can be formulated using subproblems as follows Subproblem Determine the maximum revenue obtaina... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these algorithms questions
-
Explain Canada's "points" system. Identify the reasons for which a person may have their citizenship status revoked. What is a Labour Market Impact Assessment (LMIA)? Do temporary foreign workers...
-
Carol Harris, Ph.D, CPA, is a single taxpayer and she lives at 674 Yankee Street, Durham, NC 27409. Her Social Security number is 793-52-4335. Carol is an Associate Professor of Accounting at a local...
-
After many years of amateur status, rugby union became a professional sport in 1995. Pick one of the four major North American team sports (baseball, basketball, football, or ice hockey), and imagine...
-
Donna is a Malaysian tax resident, working as a manager in the human resource department of a telecommunication company. Her remuneration yearly salary amounted to RM82,860. Her husband, Don service...
-
If r is a rational function, use Exercise 53 to show that lim x a r(x) = r(a) for every number a in the domain of r.
-
Yogo Game: Strategy in the United States - What is Yogo Game's potential for success in the U.S. market? Use a strengths, weaknesses, opportunities, and threats (SWOT) analysis as a basis for your...
-
Use stepwise regression with \(F_{\mathrm{IN}}=F_{\text {OUT }}=4.0\) to find the "best" set of regressor variables for the Belle Ayr liquefaction data in Table B.5. Repeat the analysis with...
-
The cash flow statement categorizes like transactions for optimal reporting. Identify each of the following transactions as one of the following: Operating activity (O) Investing activity (I) ...
-
Units Beginning work in process inventory 32,000 Percent Complete 65% Percent Complete 35% Units started this period 410,000 Completed and transferred out 412,000 Ending work in process inventory...
-
The adjusted trial balance columns of the worksheet for Auburn Company are as follows. Instructions Complete the worksheet. Auburn Company Worksheet (partial) For the Month Ended April 30, 2020...
-
(c) Use MegaStat or Minitab to calculate estimated seasonal indexes and trend. (Round your answers to 3 decimal places.) Qtr1 Index Qtr2 Index Qtr3 Index Qtr4 Index
-
How do the findings of behavioral economics undermine the assumptions of the standard model as to the nature of human beings? (Radical)
-
True or false? If a game has a Nash equilibrium, that equilibrium will be the equilibrium that we expect to observe in the real world.
-
If you were an economist for a firm that wanted to merge, would you argue that the three-digit or five-digit NAICS industry is the relevant market? Why?
-
Do you believe that women will arrive at different outcomes than men when playing a strategic game? Why? Which is preferable? (Feminist)
-
How do platform businesses change the nature of antitrust policy?
-
A kinematic chain is known as a mechanism when Select one: A. one link is fixed B. Three links is fixed C. two links is fixed D. none of the links is fixed
-
10m solution. If Ka(HA) = 10 then pOH of solution will be [Given : log4=0.6] (A) 6.7 (B) Greater than 6.7 & less than 7.0 (C) Greater 7.0 & less than 7.3 (D) Greater than 7.3
-
Harold Conners (Social Security number 785-23-9873) lives at 13234 DeMilo Drive, Houston, TX 77052, and is self-employed for 2012. He estimates his required annual estimated tax payment for 2012 to...
-
Walter, a single taxpayer, purchased a limited partnership interest in a tax shelter in 1985. He also acquired a rental house in 2012, which he actively manages. During 2012, Walter's share of the...
-
Janie graduates from high school in 2012 and enrolls in college in the fall. Her parents pay $4,000 for her tuition and fees. a. Assuming Janie's parents have AGI of $170,000, what is the American...
-
If you look at the light spectrum reflected from the surface of a DVD compared to the spectrum reflected from the surface of a CD, youll see that the rainbows from the DVD are more spread out, with...
-
Increasing the density of a material tends to increase the index of refraction. Does light travel faster in seawater or in fresh water?
-
Antireflection coatings for glass usually have an index of refraction that is less than that of glass. Explain how this permits a thinner coating.
Study smarter with the SolutionInn App