%problem 172.
%
%In this optimization problem, the student is given a function F and a set of 
%inequalities. The student is asked to enter
%
%N=(number of slack variables which must be added), and
%M=(maximum number of basic solutions there could be).
%
%These are checked and then explained. The augmented matrix A for the problem
%has been entered for the student, who must find and record all non-negative
%solutions.
%The student is then required to record the maximum value of the function F
%and the vertex at which it occurs. The problem ends, but to help the student
%with evaluating the value of F at any point, a matrix C has been entered such
%that entering
%
%    F=X*C
% 
%for any user-defined 1*3 vector will calculate the value of F at X.

clear variables

global undo;
global hintnumber
global noprint;
global err;
err=0;
noprint=0;

hintnumber=172;
N=0;
M=0;
r='nothing'; %this prevents Matlab error on first pass of while loop

A=[1 1 1 0 0 10;-1 2 -1 1 0 8;2 2 -4 0 1 14]; %augmented matrix pre-entered for user.
C=[14;16;15];

clc

sprintf('%s\n\n%s\n\n%s\n\n%s\n\n%s\n\n%s\n\n%s\n\n\n%s \n\n%s','Problem 172.','In this problem you will find the maximum value of','     F(X1,X2,X3) = 14 X1  +  16 X2  + 15 X3','subject to the constraints:','        X1  +   X2  +   X3  =  10','      -X1  +  2 X2  -   X3 <=   8','      2 X1  + 2 X2  - 4 X3 <=  14','      X1 >= 0,  X2 >= 0,  X3 >= 0.','press RETURN for more')

input(' '); %wait for return
sprintf('%s\n%s\n\n%s\n%s\n\n%s','How many slack variables must be added ?','Enter the number as N= ... ','What is the maximum number of basic solutions there could be ?','Enter the number as M= ...','Enter "discuss" to have your answers checked')


while(strcmp(r,'stop')==0)  %outer loop
  r=input('problem 172>>','s');

    if (strcmp(r,'stop')==1)
     return
    end


    if (findstr(r,'discuss')>=1)
          if (N==2 & M==10)  
              clc
              sprintf('%s\n\n%s\n\n%s\n%s\n%s\n%s\n%s\n%s\n\n%s','Correct !','  N=2.  (note that there is no need to add a slack variable for an equality)','  M=10.  There are','       5','      C = 10','       3','possible basic solutions, as there are 5 variables and 3 equations','(and so 3 pivots)','press RETURN for more')
          else
              clc
              sprintf('%s\n\n%s\n\n%s\n%s\n%s\n%s\n%s\n%s\n\n%s','One or both are incorrect:','N=2.  (note that there is no need to add a slack variable for an equality)','M=10.  There are','       5','      C = 10','       3','possible basic solutions, as there are 5 variables and 3 equations','(and so 3 pivots)','press RETURN for more')
          end  
                  input(' '); %wait for return
                    clc
                  sprintf('%s\n%s\n\n%s\n%s','The augmented matrix for this problem, A,  has already been entered for you.','Find and record all non-negative solutions.','Enter "discuss" when you have done this, or "stop" to leave the problem.','(remember that you can print A on the screen just by entering "A")')
                   
                       while(strcmp(r,'stop')==0)  %inner while loop begin
                            r=input('problem 172>>','s');

                         if (strcmp(r,'stop')==1)
                           return
                         end


                        if (findstr(r,'discuss')>=1)
                         clc
                         sprintf('%s\n%s\n\n%s\n%s\n\n%s\n\n%s\n\n%s\n\n%s\n%s\n\n%s\n\n%s','Record the maximum value of F and the vertex at which','it occurs as your answer to this question.','To help you with this task, Matlab will calculate F for you','if you enter the values X1, X2, X3 in a row vector called X,','     ie: X=[X1 X2 X3]   (Matlab syntax)','and then enter:','         F=X*C','where C has also already been entered for you, and is a column','vector containing the coefficients of of the function F(X1,X2,X3)','ie: C=[14;16;15] has been entered for you.','(end of problem 172)')  
                         
                        

    
                               return  %end of problem 172, return to main environment
                        
                        elseif (findstr(r,'hint')>=1)
                          hint

                        else
                           eval(r,'errormessage')
                           noprint=0; %resets error suppression
                           err=0;   
                        end  
                      end %inner while loop end
    

    elseif (findstr(r,'hint')>=1)
    hint  %call hint file

    else
     eval(r,'errormessage')
     noprint=0; %resets error suppression
     err=0;             

  end %if-else loop end

end %while loop end