// Example problem of sensitivity analysis - changes in RHS 

//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
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// Author: Remya Kommadath
// Organization: FOSSEE, IIT Bombay
// Email: toolbox@scilab.in
//============================================================================

clc; 

nProducts = 3;
TotalProcessingTime = 60;
RequiredTime = [6 5 8];
StokeRoomCapacity = 15000;
RequiredSpace = [10 20 10]*100;
Demand = 8; 
Revenue = [5 4.5 6];
nVar = nProducts // 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)]';
lb = zeros(1,size(Aeq,2));

[xopt,fopt,exitflag,output,lambda]=linprog(Cost, [],[], Aeq, beq, lb,[]);
clc;
select exitflag
case 0
    mprintf('The optimum solution has been found \n')
    disp(xopt(1:nVar)', "The optimum number of six-ounce juice glasses,ten-ounce fancy cocktail glasses and champagne glass")
    SlackVariables = xopt(nVar+1:length(xopt));
    disp(SlackVariables',"The surplus resource available")
    Index = find(SlackVariables>0);
    newbeq = beq(Index) - SlackVariables(Index);
    changedbeq = beq;
    changedbeq(Index) = newbeq;
    mprintf(' The value beyond %f of the RHS value of constraint number %d will not change the optima. \n ',newbeq,Index)
    mprintf('\n The optimal cost is %f',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