x1 + 2x₂ -x1 + x₂ ≤ 1 x12x₂ < 2 x1, x2 > 0 Write the initial dictionary where the basic variables are the slack variables. Find the initial basic solution. Is it feasible or not? max s. t. Does the initial dictionary show the LP problem to be unbounded or not? Plot the feasible region in the (1,2)-plane. Is the feasible region bounded? Plot the objective direction in graph obtained in (d). Is the LP problem bounded? Indicate whether each of the following general statements (not restricted to the LP given in this problem) is True or Fals 1. If an LP problem is unbounded, then its feasible region is unbounded. True or False? 2. If the feasible region of an LP problem is unbounded, then the LP is unbounded. True or False? Solve the LP using the simplex method. How can we tell from the final dictionary that the LP problem is unbounded?

x1 + 2x₂ -x1 + x₂ ≤ 1 x12x₂ < 2 x1, x2 > 0 Write the initial dictionary where the basic variables are the slack variables. Find the initial basic solution. Is it feasible or not? max s. t. Does the initial dictionary show the LP problem to be unbounded or not? Plot the feasible region in the (1,2)-plane. Is the feasible region bounded? Plot the objective direction in graph obtained in (d). Is the LP problem bounded? Indicate whether each of the following general statements (not restricted to the LP given in this problem) is True or Fals 1. If an LP problem is unbounded, then its feasible region is unbounded. True or False? 2. If the feasible region of an LP problem is unbounded, then the LP is unbounded. True or False? Solve the LP using the simplex method. How can we tell from the final dictionary that the LP problem is unbounded?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter11: Nonlinear Programming

Section11.11: Separable Programming

Problem 3P

See similar textbooks

Similar questions

I need a solution to this question quickly -Given the following search tree, apply the Expected Minmax algorithm to it and show the search tree that would be built by this algorithm. -Who is the winner player and what is his final utility value?
Single Point based Search: Fair share problem: Given a set of N positive integers S={x1, x2, x3,…, xk,… xN}, decide whether S can be partitioned into two sets S0 and S1 such that the sum of numbers in S0 equals to the sum of numbers in S1. This problem can be formulated as a minimisation problem using the objective function which takes the absolute value of the difference between the sum of elements in S0 and the sum of elements in S1. Assuming that such a partition is possible, then the minimum for a given problem instance would have an objective value of 0. A candidate solution can be represented using a binary array r=[b1, b2, b3,…, bk,… bN], where bk is a binary variable indicating which set the k-th number in S is partitioned into, that is, if bk =0, then the k-th number is partitioned in to S0, otherwise (which means bk =1) the k-th number is partitioned in to S1. For example, given the set with five integers S={4, 1, 2, 2, 1}, the solution [0,1,0,1,1] indicates that S is…
Consider the following map and the straight-line distance to the city entitled “M” from every other city. Find the shortest path from “A” to “M” using A* searching algorithm. Draw the tree structure and trace algorithm using open and closed list. Also state the shortest route with cost. Map is attached in file. H(n) value of each city is given in the following table. To calculate the final f(n) of each city use the following formula except city M. g(n)=Straight line distance(n)+66 F(n)=g(n) + H(n) Heuristic value H(n) of each city given in the following table A B C D E F G H I J K L M 223 222 166 192 165 136 122 111 100 60 32 102 0
4. What are the differences between L2 and L1 regularization? For a given linear decision (w,b), calculate the value of the L2 and L1 penalty 5. Describe majorization-minimization and gradient descent 6. Describe the proximal gradient descent method: what is the gradient step? What is the proximal step? For a set Q={x : ||x||<=1} in 2D space, what is the result of ProxQ(y) where a) y=[0.5,0.2]; b) y=[2,0]
How would you modify the dynamic programming algorithm for the coin collecting problem if some cells on the board are inaccessible for the robot? Apply your algorithm to the board below, where the inaccessible cells are shown by X’s. How many optimal paths are there for this board? You need to provide 1) a modified recurrence relation, 2) a pseudo code description of the algorithm, and 3) a table that stores solutions to the subproblems.
Using C++, code the following problem: In this problem, we are given a knapsack of fixed capacity C. We are also given a list of N objects, each having a weight W(I) and profit P(I). We can put any subset of the objects into the knapsack, as long as the total weight of our selection does not exceed C. The goal is to maximize the total profit, which is the sum of the profits of each object we put into the knapsack. Example: Input: C = 3 W: 1 2 3 P: 100 5 50 Selected Items: 1 2 Explanation: Possible selections that can be put in the knapsack are: 1 with profit 100 2 with profit 5 3 with profit 50 1 and 2 with profit 105 Note that in this problem, there is no need that the some of weights be exactly C. Hence, in this example, 1 is a valid solution but since the profit is lower than the maximum, is not the final answer. Input Format First line is C. Second line is the number of objects, N. The next N lines, each line contains two numbers: the first number is the weight of an…
knapsack problem: given the first table: c beeing value and w beeing weight, W max weight. I got table 2 as a solution to: 2 Solve the Knapsack problem with dynamic programming. To do this, enter the numbers Opt[k,V ] for k = 1,...,5 and V = 1,...,9 in a table. Here Opt[k, V ] is the partial solution obtained for the first k items with maximum weight V. " Can somebody explain me the values of the table? How do they get calculated? Also how do i solve the followup-task: Using the values in the table, determine a solution OPTSOL(I)=(β1,β2,β3,β4), starting with β4. (Use backtracing to do this)
Given a string S[1, . . . , n] and a dictionary of strings S, return true if S[1, . . . , n] can be segmented into a space-separated sequence of one or more dictionary words. Note that the same word in the dictionary may be reused multiple times in the segmentation. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.
4. Reducibility, NP-completeness 4a. Recall that linear ax + b = 0 is reducible to the quadratic ax²+bx+c=0. Show that the quadratic ax2+bx+c=0 is reducible to quartic ax*+bx+cx+dx+e=0 (Lec14.1). Is quartic reducible to quadratic? 4b. Consider the 4-way Partition Problem: Given a set S of positive integers, determine whether S can be partitioned into four subsets S1, S2, S3, and S4 such that the sum of the numbers in S, is equal to S2, S3, and S4. Demonstrate that the problem is NP-complete based on NP-completeness of the 2-way Partition Problem. 4c. Prove that P != NP.
Run Skiena’s algorithm by hand to solve the Partial Digest Problem for ? = {1,2,3,3,4,4,5,6,7,9} to find a set ? such that ∆? = ?. Assume that the smallest element of ? is 0
Consider the following map and the straight-line distance to the city entitled “M” from every other city. Find the shortest path from “A” to “M” using A* searching algorithm. Draw the tree structure and trace algorithm using open and closed list. Also state the shortest route with cost. H(n) value of each city is given in the following table. To calculate the final f(n) of each city use the following formula except city M. g(n)=Straight line distance(n)+last two digits of your registration number i-e 58 F(n)=g(n) + H(n) Heuristic value H(n) of each city given in the following table A B C D E F G H I J K L M 223 222 166 192 165 136 122 111 100 60 32 102 0
Consider the following map and the straight-line distance to the city entitled “M” from every other city. Find the shortest path from “A” to “M” using A* searching algorithm. Draw the tree structure and trace algorithm using open and closed list. Also state the shortest route with cost. (PICTURE) H(n) value of each city is given in the following table. To calculate the final f(n) of each city use the following formula except city M. g(n)=Straight line distance(n)+last two digits of your registration number F(n)=g(n) + H(n) Heuristic value H(n) of each city given in the following table A B C D E F G H I J K L M 223 222 166 192 165 136 122 111 100 60 32 102 0