In the initial solution of a transportation problem, the only restriction is that there should be non zero quantities in a majority of the boxes when all constraints must be satisfied. demand must equal supply. we must have a number which is equal to the number of rows plus the number of columns minus one of boxes which contain non zero quantities. all constraints must not be satisfied.
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- IP Applications 4 Employment for Projects Formulate the following problem as integer linear programming problem. A company hires employees from a pool of 80 people. Employees are hired on a day to day basis. The pool contains 25 experienced persons. An experienced person can do twice as much work as an inexperienced person in the same time. Our company has n projects for which it has to recruit people. For the upcoming T days employees have to be divided over the projects. For project i (i = 1; :::; n) is w, the amount of required work on day t (t = 1; :::; T); an inexperienced employee can perform one unit of work per day. If an employee is hired on a certain day, he/she works on the same project all day. The cost for hiring a normal employee are c, per day and the cost for hiring an experienced employee are c, per day. Finally, for every day the minimal number of experienced employees that has to work on project i equals u,. The company wants to minimize the cost of hiring employees.…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 18Maximum weight = 20The above problem is a 0/1 Knapsack problem. Here there are 7 different objects labelled from A to G. The objective of this problem is to carry the different objects in your bag in such a way such that the profit is maximized. But you have to make sure that your bag does not exceed the maximum weight i.e. the maximum weight that this bag can carry is less than or equal to 15. Remember you can carry an object exactly once. Now it is your job to use Genetic Algorithm to solve this problem. 1. Encode the problem and create an initial population of 4 different chromosomes 2. Think of an appropriate fitness function to this problem and give proper justification. 3. Use the fitness function to calculate the fitness level of all the chromosomes in your population 4. Perform natural selection and select the two fittest chromosomes 5. Use the parents from (4) and perform crossover to get 2 offspring 6. Perform mutation and check the fitness of the final offspring. Comment…
- 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.Application of DFA minimization: Choose a DFA minimation problem that is unique. Your DFA to minimize must have at least 5 states, cannot already be minimal, and cannot be a solved problem from any book. You should describe the DFA, the process to minimize it, and the minimized DFA.Assignment problem (Hungarian Method) · Example 2: A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites %3D are given below. Bulldozer/ A В C D Site Students 1 90 75 75 80 solve it yourself 2 35 85 55 65 3 125 95 90 105 4 45 110 95 115 How should the bulldozers be moved to the construction sites in order to minimize the total distance traveled?
- Computer Science An IT company has branches in 10 cities. In each of the cities, it employs 5 employees. The company carries out 10 different projects and employs 5 employees in each of the projects (not necessarily from the same city). Each employee works in exactly one of the projects. Show that one can choose a group of 10 employees so that there is one employee from each city and one employee from each project in this group.Current Attempt in Progress The accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery. 200 E X3 D 150 X5 X₁' 200 25 A B x2 175 C (a) Set up a linear system whose solution provides the unknown flow rates. 25 X2 175 X3 Find A so that Ax=y where = and y = 200 THO 150 200 Form the system so that the first equation represents node A, the second equation node B, etc. Then take all the variable to one side such that all the constants are on one side and positive. From the equations form the required matrices and enter the appropriate values for A below. A =Limits 15, 128 MB We all know about the recent flood in Sylhet. Every area of Sylhet can be expressed with a number. If there are n number of areas in Sylhet then they can be expressed as 1, 2, 3...n-1,n. Where the area is located after the (1) area. Volume of each area of Sylhet is 1 meter. A few dams have been constructed in certain areas in Sylhet. Each dam is pre-planned to be built at a certain height so that the flood water cannot completely inundate the city Flood water will enter through the 1, area. The height of the dam in the area is B, meter. If the water level in area i is greater than B meter then the remaining water will flow in (i+1), area. Due to the good communication system of Sylhet, people can move from one area to another before any danger Sylhet is the city of rain. Every area has some tall buildings built to deal with the flood problem. The building in the fen area has H, floors and each floor has a height of 1meter. Due to the weather forecast people can know…
- A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 9 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? Your answer is:Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution. A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows: - Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram. The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber. The farm wishes to determine the optimum ratios of corn and soybeans to produce a feed with minimal costs while maintaining nutritional constraints and ensuring that a minimum of 800 grams of feed is used daily. Restrictions 1. The total amount of feed should be at least 800 grams per day.2. The feed should contain at least 30% protein…At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . ,the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the priceof $2.50 per kg. He leaves the rest of the grapes in storage where each day they dryout a little so that their weight decreases by 3%. Let wn be the weight (in kg) ofthe stored grapes at the beginning of day n for n ≥ 1 (before he takes any to themarket).(a) Find the value of wn for n = 2.(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)(c) Let rn be the total revenue (in dollars) earned from the stored grapes from thebeginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursiveformula for rn.(d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num wherenum is entered by the user, and display the values in three columns: n, wn, rnwith appropriate headings.Run the program for num =…