

#define N 6  						// Number of individual family farms
#define EPSILON .000001
#define TXBILL 7.5					// In thousands of dollars

continuous Tax[N]; 
continuous Z[N];					// Z[j] is the bound for the jth appli-
								// cation of the Flat Covering Theorem
int count;    
int flag[N];    

#define OFF 0
#define ON 1
body_of_the_loop(continuous Z)
{
	and(int i=0;i<N;i++)
		if flag[i] == OFF;
		then Z >= Tax[i];
        
	min: Z; 
	Z == wp(Z);
	and(int i=0;i<N;i++)
		if flag[i] == OFF;                
		then {
			min: Tax[i];
			if fabs(Tax[i]-Z) < EPSILON;         
			then {
			       flag[i] = ON;
			       count = count + 1;
       			}
		}
}
 
2lp_main()
{
	by_laws();
 
	// Funds required for repairs
	sigma(int i=0;i<N;i++) Tax[i] == TXBILL; 

	printf("With the naive solution we have\n");
	and(int i=0;i<N;i++) 
		printf("Tax on family farm %d is $%.2f\n",i,1000*Tax[i]);
        
	printf("\n\n");

	// Even out tax levies
	and(int j=0;count!=N;j++) 
		body_of_the_loop(Z[j]);
 
	printf("After smoothing we have \n");
	and(int i=0;i<N;i++) 
		printf("Tax on family farm %d is $%.2f\n",i,1000*Tax[i]);
}


by_laws() 
{
	// Relations among tax levies dictated by bylaws
	
	// Proximity to road
       		Tax[0] + 2*Tax[1] + 4*Tax[2] + 7*Tax[4] >= 16;

	// Proximity to silos
       		2.5*Tax[0] + 3.5*Tax[1] + 5.2*Tax[4] >= 17.5; 

	// Dwelling size
	  	0.4*Tax[1] + 1.3*Tax[3] + 7.2*Tax[5] >= 12;  
	// Size of acreage 
       		2.5*Tax[1] + 3.5*Tax[2] + 5.2*Tax[4] >= 13.1;

	// Size of livestock facilities
		3.5*Tax[0] + 3.5*Tax[3] + 5.2*Tax[5] >= 18.2; 
}
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