How do duality concepts influence the solutions of linear programming problems?
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- How do duality principles shed light on the relationship between primal and dual solutions in integer programming?loose coupling and high cohesion at this problem ProblemDesign a class for a quadratic equation python language with class not root functionHow does the duality theorem facilitate the transformation of primal to dual problems in linear programming?
- loose coupling and high cohesion at this problem ProblemDesign a class for a quadratic equation python languageWrite a computer program for Gauss elimination method using C programming language. (NOT JAVA or C++) Don't forget to show the upper triangular matrix7. Find a closed form representation for the function defined recursively by f(1)-10 and f(n)=5ƒ(%) + n.
- 1. For the function defined recursively by f(0)=5 and f(n)=4f (n-1)+3, answer the following: a. Find a closed form representation for this function. Your closed form should not include any series. b. Prove that your representation is correct using a formal inductive argument.TROUBLESHOOTING: Fix the errors in the code below MATLAB function [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % Solves Ax = b by Gauss-Seidel method with relaxation. % USAGE: [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % INPUT: % func = handle of function that returns improved x using % x = starting solution vector % maxIter = allowable number of iterations (default is 500) % epsilon = error tolerance (default is 1.0e-9) % OUTPUT: % x = solution vector % numIter = number of iterations carried out % omega = computed relaxation factor if nargin < 4; epsilon = 1.0e-9; end if nargin < 3; maxIter = 500; end k = 10; p = 1; omega = 1; for numIter = 1:maxIter xOld = x; x = feval(func,x,omega); dx = sqrt(dot(x - xOld,x - xOld)); if dx < epsilon; return; end if numIter == k; dx1 = dx; end if numIter == k + p omega = 2/(1 + sqrt(1 - (dx/dx1)ˆ(1/p))); end end error(’Too many iterations’)How does the principle of duality provide insights into the complementary slackness condition in linear programming?