Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Chapter 4.10, Problem 5P
Explanation of Solution
LINGO output
- LINGO is an optimization modelling language that enables user to create many constraints or objective function terms by typing one line.
- LINGO is used to solve both linear and nonlinear problems.
- It is a software tool which is designed efficiently for building and solving linear, nonlinear and integer optimization.
- The LINGO model consists of three parts which are objective function, variables and constraints.
- The objective function is a formula that describes what the model optimizes exactly.
- Variables are the quantities that can be changed for producing the optimal value of the objective function.
- The constraint is the formula that defines the limits on the values of the variables...
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Suppose that a manufacturing company builds n different types of robots, sayrobots 1, 2, . . . , n. These robots are made from a common set of m types of materials, saymaterials 1, 2, . . . , m. The company has only a limited supply of materials for each year,the amount of materials 1, 2, . . . , m are limited by the numbers b1, b2, . . . , bm, respectively.Building robot i requires an aij amount from material j. For example, building robot 1requires a11 from material 1, a12 from material 2, etc. Suppose the profit made by sellingrobot i is pi.
Write an integer linear program for maximizing the annual profit for thecompany
This is an algorithmic graph problem.
Consider a set of movies M1, M2, ... , Mk. There is a set of customers, each one of which indicates the two movies they would like to see this weekend. Movies are shown on Saturday evening and Sunday evening. Multiple movies may be screened at the same time.
You must decide which movies should be televised on Saturday and which on Sunday, so that every customer gets to see the two movies they desire. Is there a schedule where each movie is shown at most once? Design an efficient algorithm to find such a schedule if one exists.
A local merchant goes to a market to buy apples with 500 UM. They offer two types of apples: green ones at 0.5 UM per kg and red ones at 0.8 UM per kg. We know that he only has space in his van to transport a maximum of 700 kg of apples and that he plans to sell a kilo of green apples for 0.58 UM and red apples for 0.9 UM. Graph this operations research problem.- How many kilograms of apples of each type should you buy to obtain maximum profit?
Chapter 4 Solutions
Operations Research : Applications and Algorithms
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.4 - Prob. 1PCh. 4.4 - Prob. 2PCh. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Prob. 5PCh. 4.4 - Prob. 6PCh. 4.4 - Prob. 7P
Ch. 4.5 - Prob. 1PCh. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - Prob. 7PCh. 4.6 - Prob. 1PCh. 4.6 - Prob. 2PCh. 4.6 - Prob. 3PCh. 4.6 - Prob. 4PCh. 4.7 - Prob. 1PCh. 4.7 - Prob. 2PCh. 4.7 - Prob. 3PCh. 4.7 - Prob. 4PCh. 4.7 - Prob. 5PCh. 4.7 - Prob. 6PCh. 4.7 - Prob. 7PCh. 4.7 - Prob. 8PCh. 4.7 - Prob. 9PCh. 4.8 - Prob. 1PCh. 4.8 - Prob. 2PCh. 4.8 - Prob. 3PCh. 4.8 - Prob. 4PCh. 4.8 - Prob. 5PCh. 4.8 - Prob. 6PCh. 4.10 - Prob. 1PCh. 4.10 - Prob. 2PCh. 4.10 - Prob. 3PCh. 4.10 - Prob. 4PCh. 4.10 - Prob. 5PCh. 4.11 - Prob. 1PCh. 4.11 - Prob. 2PCh. 4.11 - Prob. 3PCh. 4.11 - Prob. 4PCh. 4.11 - Prob. 5PCh. 4.11 - Prob. 6PCh. 4.12 - Prob. 1PCh. 4.12 - Prob. 2PCh. 4.12 - Prob. 3PCh. 4.12 - Prob. 4PCh. 4.12 - Prob. 5PCh. 4.12 - Prob. 6PCh. 4.13 - Prob. 2PCh. 4.14 - Prob. 1PCh. 4.14 - Prob. 2PCh. 4.14 - Prob. 3PCh. 4.14 - Prob. 4PCh. 4.14 - Prob. 5PCh. 4.14 - Prob. 6PCh. 4.14 - Prob. 7PCh. 4.16 - Prob. 1PCh. 4.16 - Prob. 2PCh. 4.16 - Prob. 3PCh. 4.16 - Prob. 5PCh. 4.16 - Prob. 7PCh. 4.16 - Prob. 8PCh. 4.16 - Prob. 9PCh. 4.16 - Prob. 10PCh. 4.16 - Prob. 11PCh. 4.16 - Prob. 12PCh. 4.16 - Prob. 13PCh. 4.16 - Prob. 14PCh. 4.17 - Prob. 1PCh. 4.17 - Prob. 2PCh. 4.17 - Prob. 3PCh. 4.17 - Prob. 4PCh. 4.17 - Prob. 5PCh. 4.17 - Prob. 7PCh. 4.17 - Prob. 8PCh. 4 - Prob. 1RPCh. 4 - Prob. 2RPCh. 4 - Prob. 3RPCh. 4 - Prob. 4RPCh. 4 - Prob. 5RPCh. 4 - Prob. 6RPCh. 4 - Prob. 7RPCh. 4 - Prob. 8RPCh. 4 - Prob. 9RPCh. 4 - Prob. 10RPCh. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 16RPCh. 4 - Prob. 17RPCh. 4 - Prob. 18RPCh. 4 - Prob. 19RPCh. 4 - Prob. 20RPCh. 4 - Prob. 21RPCh. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - Prob. 24RPCh. 4 - Prob. 26RPCh. 4 - Prob. 27RPCh. 4 - Prob. 28RP
Knowledge Booster
Similar questions
- Consider a set of movies M1, M2, ... , Mk. There is a set of customers, each one of which indicates the two movies they would like to see this weekend. Movies are shown on Saturday evening and Sunday evening. Multiple movies may be screened at the same time. You must decide which movies should be televised on Saturday and which on Sunday, so that every customer gets to see the two movies they desire. Is there a schedule where each movie is shown at most once? Design an efficient algorithm to find such a schedule if one exists.arrow_forwardwhere a is the start node and e is the goal node. The pair [f, h] at each node indicates the value of the f and h functions for the path ending at that node. Given this information, what is the cost of each path? The cost < a, c >= 2 is given as a hint. Is the heuristic function h admissible? Explainarrow_forwarda. Given n items, where each item has a weight and a value, and a knapsack that can carry at most W You are expected to fill in the knapsack with a subset of items in order to maximize the total value without exceeding the weight limit. For instance, if n = 6 and items = {(A, 10, 40), (B, 50, 30), (C, 40, 80), (D, 20, 60), (E, 40, 10), (F, 10, 60)} where each entry is represented as (itemIdi, weighti, valuei). Use greedy algorithm to solve the fractional knapsack problem. b. Given an array of n numbers, write a java or python program to find the k largest numbers using a comparison-based algorithm. We are not interested in the relative order of the k numbers and assuming that (i) k is a small constant (e.g., k = 5) independent of n, and (ii) k is a constant fraction of n (e.g., k = n/4). Provide the Big-Oh characterization of your algorithm.arrow_forward
- A book salesperson living in New York needs to visit clients in Utah, Jersey, LA, and Milan within a month. The distances between these cities are given in the table in the picture. Solve the problem with the nearest neighbor heuristic.arrow_forwardA seller has an indivisible asset to sell. Her reservation value for the asset is s, which she knows privately. A potential buyer thinks that the assetís value to him is b, which he privately knows. Assume that s and b are independently and uniformly drawn from [0, 1]. If the seller sells the asset to the buyer for a price of p, the seller's payoff is p-s and the buyer's payoffis b-p. Suppose simultaneously the buyer makes an offer p1 and the seller makes an offer p2. A transaction occurs if p1>=p2, and the transaction price is 1/2 (p1 + p2). Suppose the buyer uses a strategy p1(b) = 1/12 + (2/3)b and the seller uses a strategy p2(s) = 1/4 + (2/3)s. Suppose the buyer's value is 3/4 and the seller's valuation is 1/4. Will there be a transaction? Explain. Is this strategy profile a Bayesian Nash equilibrium? Explain.arrow_forwardGiven R=ABCDEFGand F = {CF→B, B→C, FB→E, CBE→F, E→AG, FA→B,BG→FE, BA→CG}The following is a minimal cover: A. (CFD, FBD, BED, BAD, BDG) B. CFD→BEAG C. CF→B, FB→E, E→AG, FA→B, BA→G D. CF→B, B→C, FB→E, E→AG, FA→B, BG→F, BA→Garrow_forward
- Q-1. Consider the Farmer-Wolf-Goat-Cabbage Problem described below: Farmer-Wolf-Goat-Cabbage Problem There is a farmer with a wolf, a goat and a cabbage. The farmer has to cross a river with all three things. A small boat is available to cross the river, but farmer can carry only one thing with him at a time on the boat. In the absence of farmer, the goat will eat the cabbage and wolf will eat the goat. How can the farmer cross the river with all 3 things? State Space Formulation of the Problem State of the problem can be represented by a 4-tuple where elements of the tuple represent positions of farmer, wolf, goat and cabbage respectively. The position of boat is always same as the position of farmer because only farmer can drive the boat. Initial state: (L, L, L, L) Operators: 1. Move farmer and wolf to the opposite side of river if goat and cabbage are not left alone. 2. Move farmer and goat to the opposite side of river. 3. Move farmer and cabbage to the opposite…arrow_forwardConsider the search problem represented in Figure, where a is the start node and e is the goal node. The pair [f, h] at each node indicates the value ofthe f and h functions for the path ending at that node. Given this information, what is the cost ofeach path?1. The cost < a, c >= 2 is given as a hint.2. Is the heuristic function h admissible? Explainarrow_forwardGiven webpages {A, E, F} and links {A→F, F→A, F→E, E→F, A→E}. Then, the PageRankPr of a website Xiis calculated withPr(Xi) = (1 − d) + d(PXj→XiP r(Xj )out(j))where out(j) denotes the number of outgoing links from a webpage Xj . Understand thisproblem as an equation system problem and assume d = 0.5. What are then the estimatedPagerank values of the nodes A, E, F?arrow_forward
- Correct answer will upvoted else downvoted. segment of place where there is length n there are k climate control systems: the I-th climate control system is set in cell artificial intelligence (1≤ai≤n). At least two climate control systems can't be put in a similar cell (for example all man-made intelligence are particular). Each climate control system is characterized by one boundary: temperature. The I-th climate control system is set to the temperature ti. Illustration of portion of length n=6, where k=2, a=[2,5] and t=[14,16]. For every cell I (1≤i≤n) discover it's temperature, that can be determined by the equation min1≤j≤k(tj+|aj−i|), where |aj−i| means outright worth of the distinction aj−i. As such, the temperature in cell I is equivalent to the base among the temperatures of forced air systems, expanded by the separation from it to the cell I. How about we take a gander at a model. Consider that n=6,k=2, the main forced air system is put in cell a1=2 and…arrow_forwardCorrect answer will be upvoted else downvoted. Let C={c1,c2,… ,cm} (c1<c2<… <cm) be the arrangement of individuals who hold cardboards of 'C'. Let P={p1,p2,… ,pk} (p1<p2<… <pk) be the arrangement of individuals who hold cardboards of 'P'. The photograph is acceptable if and provided that it fulfills the accompanying requirements: C∪P={1,2,… ,n} C∩P=∅. ci−ci−1≤ci+1−ci(1<i<m). pi−pi−1≥pi+1−pi(1<i<k). Given a cluster a1,… ,an, kindly track down the number of good photographs fulfilling the accompanying condition: ∑x∈Cax<∑y∈Pay. The appropriate response can be huge, so output it modulo 998244353. Two photographs are unique if and provided that there exists no less than one individual who holds a cardboard of 'C' in one photograph yet holds a cardboard of 'P' in the other. Input Each test contains numerous experiments. The main line contains the number of experiments t (1≤t≤200000). Depiction of the experiments follows. The…arrow_forwardConsider the following problem: You are baby-sitting n children and have m > n cookies to divide between them. You must give each child exactly one cookie (of course, you cannot give the same cookie to two different children). Each child has a greed factor gi, 1 ≤ i ≤ n which is the minimum size of a cookie that the child will be content with; and each cookie has a size sj , 1 ≤ j ≤ m. Your goal is to maximize the number of content children, i.e.., children i assigned a cookie j with gi ≤ sj. Give a correct greedy algorithm for this problem, prove that it finds the optimal solution, and give an efficient implementation.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole