Maximizing the area of a polygon using string based input

/***********************************************************************
   Xpress Optimizer Examples
   =========================

   file Polygon_textformula.c
   ``````````````````````````
   Implement the polygon example using text formulas     

   Maximize the area of polygon of N vertices and diameter of 1
   The position of vertices is indicated as (rho,theta) coordinates  
   where rho denotes the distance to the base point   
   (vertex with number N) and theta the angle from the x-axis.        
   The nonlinear expressions are described text based input.

   (c) 2017 Fair Isaac Corporation       
***********************************************************************/

#include 
#include 
#include 
#include 

#include "xprs.h"
#include "xslp.h"

#define MAXROW 20
#define MAXCOL 20
#define MAXELT 50

void XPRS_CC XSLPMessage(XSLPprob my_prob, void *my_object, char *msg,
  int len, int msg_type);

int main(int argc, char *argv[]) {
  XPRSprob xprob = NULL;
  XSLPprob sprob = NULL;

  int nRow, nCol, nSide, nElement, nRowName, nColName;
  int iRow;
  char RowType[MAXROW];
  double RHS[MAXROW], OBJ[MAXCOL], Element[MAXELT], Lower[MAXCOL], Upper[MAXCOL];
  int ColStart[MAXCOL+1], RowIndex[MAXELT];
  double Factor;
  int ReturnValue;
  int i, j;
  char RowNames[500], ColNames[500];
  char *CoefBuffer;
  int BufferPos;

/* Initialisation */
  CoefBuffer = NULL;
  if (ReturnValue=XPRSinit(NULL)) goto ErrorReturn;
  if (ReturnValue=XSLPinit()) goto ErrorReturn;
  if (ReturnValue=XPRScreateprob(&xprob)) goto ErrorReturn;
  if (ReturnValue=XSLPcreateprob(&sprob,&xprob)) goto ErrorReturn;

/* XSLPsetcbmessage */
  XSLPsetcbmessage(sprob,XSLPMessage,NULL);

  nSide = 5;
  nRowName = 0;

/* Rows */
  nRow = nSide-2 + (nSide-1)*(nSide-2)/2 + 1;
  for (i=0;i 1) {
	    Element[nElement] = 1;
	    RowIndex[nElement++] = iRow;
	  }
	  iRow++;
  }

  Upper[nCol-1] = 3.1415926;

/* Equals column */
  nColName = nColName + 1 + sprintf(&ColNames[nColName],"=");
  ColStart[nCol] = nElement;
  Lower[nCol] = Upper[nCol] = 1.0; /* fixed at 1.0 */
  nCol++;

/* Remaining columns come later */
  for (i=1;i 1) {
	    BufferPos = BufferPos + sprintf(&CoefBuffer[BufferPos]," + ");
	  }
	  BufferPos = BufferPos + sprintf(&CoefBuffer[BufferPos],
                                      "RHO%d * RHO%d * SIN ( THETA%d - THETA%d )",i+1,i,i+1,i);
  }
  XSLPchgccoef(sprob,0,nSide,&Factor,CoefBuffer);

/* Distances */
  Factor = 1.0;
  for (i=1;i