Consider the following network representation of a transportation problem. Des Moines 25 15 Jefferson 30 City Kansas 15 City 11 Omaha St. Louis 30 Supplies Demands The supplies, demands, and transportation costs per unit are shown on the network. (a) Develop a linear programming model for this problem; be sure to define the variables in your model. Let X- amount shipped from Jefferson City to Des Moines X12- amount shipped from Jefferson City to Kansas City * amount shipped from Jefferson CRy to St. Louis X- amount shipped from Omaha to Des Moines Xa- amount shipped from Omaha to Kansas City X amount shipped from Omaha to St. Louis Min S.t. *12 *12 (b) Solve the inear program to determine the optimal solution. Amount Cost Jefferson City-Des Moines Jefferson City-Kansas City Jefferson City-St. Louis Omaha-Des Moines Omaha-Kansas City Omaha-St. Louis Total

Consider the following network representation of a transportation problem. Des Moines 25 15 Jefferson 30 City Kansas 15 City 11 Omaha St. Louis 30 Supplies Demands The supplies, demands, and transportation costs per unit are shown on the network. (a) Develop a linear programming model for this problem; be sure to define the variables in your model. Let X- amount shipped from Jefferson City to Des Moines X12- amount shipped from Jefferson City to Kansas City * amount shipped from Jefferson CRy to St. Louis X- amount shipped from Omaha to Des Moines Xa- amount shipped from Omaha to Kansas City X amount shipped from Omaha to St. Louis Min S.t. 12 12 (b) Solve the inear program to determine the optimal solution. Amount Cost Jefferson City-Des Moines Jefferson City-Kansas City Jefferson City-St. Louis Omaha-Des Moines Omaha-Kansas City Omaha-St. Louis Total

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

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The public utilities commission has decided that the electric company overcharged its customers for two months last year. To make up the difference to the customers, the commission orders the company to decrease each of the next month’s bills by 10%. The city also levies a 3%utility tax, which is to be applied to the bill before it is discounted. Also, the10% discount does not apply to the utility tax. Assume electricity costs $0.16per kilowatt-hour. Write a program to compute the next month’s electricity bill given the number of kilowatt-hours consumed as input
Intersections in England are often constructed as one-way "roundabouts," such as the one shown in the figure. Assume that traffic must travel in the directions shown. Find the general solution of the network flow. Find the smallest possible value for X8- X₁ = X3 X4 = X5 X is free X₁ = X₂ is free X₂ = X4 = X5 is free X8 is free 60 >>> Find the smallest possible value for xg. The smallest possible value for X is 100 B, *24 A X₁ 120 140 %3 What is the general solution of the network flow? Choose the correct answer below and fill in the answer boxes to complete your choice. A. B. C. D. x₁ is free is free x2 = X₂ is free X₂ is free X5 = X is free D * *1 E x5 F -80 100 X₂ sm X4 = 5 X is free
4. Consider the Railway Reservation System. There are a number of trains and each train stops in one or more stations. Each train has a predetermined number of seats available in each of classes (First class, First AC, Second AC, Third AC, Sleeper and so on). The fare between two stations is determined by the class of travel and the distance. Passenger can enquire about the availability of seats between any two stations and for any class. The Railway Reservation System should be able to handle the queries and perform the necessary reservation/ cancellation operations. Draw a class diagram for the case study.
In a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet.
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
Knapsack 0/1 problem: Given N items where each item has some weight and profit associated with it and also given a bag with capacity W, [i.e., the bag can hold at most W weight in it]. The task is to put the items into the bag such that the sum of profits associated with them is the maximum possible. Given the problem is solved using a dynamic programming approach and the matrix derived is given below, answer the below set of questions by analyzing the DP matrix. weights = [2, 3, 4, 5], profits = [1, 2, 5, 6], Capacity W = 8 Capacity 2 3 Profits weights|0 1 2 5 16 14 |-> 5 10 0 O 10 1 2 3 4 0 O 0 1 1 0 1 0 1 O 10 1 2 2 2 5 2 O 15 50 1 356 6 O 1 3 6 18 00378 7 10 10 1 3 7 7 1 18
More and more seafood is being farm-raised these days. A model (differentialequation) used for the rate of change for a fish population, P(t) in farmingponds is given by P'(t) = b(1-(P(t)/Pm)) - hP(t) where b is the birth rate, PM is the maximum number of fish the pond cansupport, and h is the rate the fish are harvested. Write a python code that implements the Forward Euler method to solve thedifferential equation Suppose that the carrying capacity PM = 20, 000 fish with a birth rateof 6% and a harvesting rate of h = 0%, use your Python code to findand plot the numerical solution for the first 400 days for different valuesof y0. Pick y0 < 20, 000, y0 > 20, 000. Don’t forget to label all your plotswith x and y axes label, titles and legends. Use a time step ∆t = 0.1
Problem 3: A day at the beach. A group of n people are lying on the beach. The beach is represented by the real line R and the location of the i-th person is some integer r; e Z. Your task is to prevent people from getting sunburned by covering them with umbrellas. Each umbrella corresponds to a closed interval I = [a, a + L] of length L e N, and the i-th person is covered by that umbrella if æ¡ € I. Design a greedy algorithm for covering all people with the minimum number of umbrellas. The input consists of the integers x1,..., En, and L. The output of your algorithm should be the positions of umbrellas. For example, if the input is r1 = 1, x2 = 3, r3 = 5, and L = 2, then an optimum solution is the set of two umbrellas placed at positions 2 and 5, covering intervals [1,3] and [4,6]. 1 2 3 4 5 6 Prove that your algorithm is correct and that it runs in time polynomial in n.
Classes are scheduled at a school. Once students have submitted their course requests, a computer algorithm can determine the optimal schedule for everyone. The school has concluded that it will take too long to determine the best schedule. Instead, they resort to a less sophisticated method that produces a serviceable if not ideal timetable. Which guiding concept is represented here?
A city would like to know how many vehicles it could move through its streets in an emergency. The most likely situa evacuation starting at the school and ending at the park. The connections between these two locations, plus their cap direction, is shown below. C Oak Street 1" Street F School Park B Elm Jad Street Street E A Path Capacity Б C D 30 20 E F 25 25 30 25 20 (Round your answer to the nearest whole number.) Maximum Flow
A circus is preparing a tower performance in which people stand on top of each other's shoulders. For practical and aesthetic reasons, each individual must be both shorter and lighter than the person below him or her. Develop a formula to calculate the maximum number of people that can fit in such a tower given the heights and weights of each participant in the circus.A circus is preparing a tower performance in which people stand on top of each other's shoulders. For practical and aesthetic reasons, each individual must be both shorter and lighter than the person below him or her. Develop a formula to calculate the maximum number of people that can fit in such a tower given the heights and weights of each participant in the circus.
Q : Draw a flow chart for the following problem. Compute electricity bill using the following rates:i : First 100 units cost Rs 7.00 per unitii : Next 50 units cost Rs 10.00 per unitiii : All other units cost Rs 15.00 per unit