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+// Example problem for sensitivity analysis - using duality theorem to determine the reduced cost
+
+//Reference : Bradley, Hax, and Magnanti,"Applied Mathematical Programming", Addison-Wesley, 1977, chapter 3 
+
+//A custom molder has one injection-molding machine and two different dies to fit the machine. Due to differences in number of cavities and cycle times, withthe first die he can produce 100 cases of six-ounce juice glasses in six hours,while with the second die he can produce 100 cases of ten-ounce fancy cocktail glasses in five hours. The molder is approached by a new customer to produce a champagne glass. The production time for the champagne glass is 8 hours per hundred cases. He prefers to operate only on a schedule of 60 hours of production per week. He stores the week’s production in his own stockroom where he has an effective capacity of 15,000 cubic feet. A case of six-ounce juice glasses requires 10 cubic feet of storage space, while a case of ten-ounce cocktail glasses requires 20 cubic feet due to special packaging.The storage space required for the champagne glasses is 10 cubic feet per one case. The contribution of the six-ounce juice glasses is $5.00 per case; however, the only customer available will not accept more than 800 cases per week. The contribution of the ten-ounce cocktail glasses is $4.50 per case and there is no limit on the amount that can be sold where as the contribution of champagne glasses is $6.00 per case with no limit on the bound. How many cases of each type of glass should be produced each week in order to maximize the total contribution?
+//=============================================================================
+// Copyright (C) 2018 - IIT Bombay - FOSSEE
+// This file must be used under the terms of the CeCILL.
+// This source file is licensed as described in the file COPYING, which
+// you should have received as part of this distribution.  The terms
+// are also available at
+// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+// Author: Remya Kommadath
+// Organization: FOSSEE, IIT Bombay
+// Email: toolbox@scilab.in
+//============================================================================
+
+clc; 
+// -----------------------------Primal model-------------------------------
+nProducts = 3;
+TotalProcessingTime = 60;
+RequiredTime = [6 5 8];
+StokeRoomCapacity = 15000;
+RequiredSpace = [10 20 10]*100;
+Demand = 8; 
+Revenue = [5 4.5 6];
+nVar = 3 // Each variable indicates number of hundreds of units of each product
+
+// Linear constraints
+// Processing time constraint
+A1 = RequiredTime;
+b1 = TotalProcessingTime;
+// Space constraint
+A2 = RequiredSpace;
+b2 = StokeRoomCapacity;
+// Demand constraint
+nDemand = length(Demand);
+A3 = eye(nDemand,nVar);
+b3 = Demand';
+
+A = [A1;A2;A3]; b = [b1;b2;b3];
+
+//Addition of slack variables
+nInEqConstraints = length(b);
+Aeq = eye(nInEqConstraints,nInEqConstraints);
+Aeq = [A Aeq];
+beq = b;
+
+Cost = -[Revenue zeros(1,nInEqConstraints)]';
+
+// -------------------------------Dual model------------------------------
+dualA = -A';
+dualb = Cost(1:nVar);
+
+dual_nInEqConstraints = length(dualb);
+dualAeq = eye(dual_nInEqConstraints,dual_nInEqConstraints);
+dualAeq = [dualA dualAeq];
+dualbeq = dualb;
+dualCost = beq;
+dualCost = [dualCost; zeros(dual_nInEqConstraints,1)];
+dual_nVar = length(dualCost);
+dual_lb = zeros(1,size(dualAeq,2));
+
+[dual_xopt,dual_fopt,dual_exitflag,dual_output,dual_lambda] = linprog(dualCost,[],[], dualAeq, dualbeq, dual_lb,[]);
+clc;
+select dual_exitflag
+case 0
+    disp(dual_xopt(1:nInEqConstraints)',"Dual values of the primal constraints")
+    disp(dual_xopt(nInEqConstraints+1:dual_nVar)',"Dual values of the primal variables")
+    TopRow = ["Variable     "  "Rate of change in optima"];
+    Table = string([(1:length(dual_xopt))' -dual_xopt]);
+    disp("The change in optima due to one unit increase in each variables are given as below")
+    disp([TopRow;Table])
+    disp(["The optimal cost is ", string(dual_fopt)])
+case 1
+    disp("Primal Infeasible")
+case 2
+    disp("Dual Infeasible")
+case 3
+    disp("Maximum Number of Iterations Exceeded. Output may not be optimal")
+case 4
+    disp("Solution Abandoned")
+case 5
+    disp("Primal objective limit reached")
+case 6
+    disp("Dual objective limit reached")
+end