
#define MONTHS 6						// Number of periods
#define KINDS 5						// Kinds of vegetable oils
#define VATREV 150						// Selling price per vat
#define STORCOST 5						// Storage cost per vat
#define INITSTOR 500						// Initial storage in vats
#define ENDSTOR 500						// Final storage in vats
#define STORCAP 1000						// Monthly storage capacity


double price[MONTHS][KINDS];								// Table 3.2
double hardness[KINDS];								// Table 3.3


#define MODES 3						// Purchase, Process or Store
#define PURC 0
#define PROC 1
#define STOR 2


continuous Plan[MONTHS][MODES][KINDS];
continuous Revenue;


#define LIMITA 250						// Limit on group A production
#define LIMITB 200						// Limit on group B production
#define A 2
#define B 3

#define LBHARD 3.0					// Lower bound on average hardness
#define UBHARD 6.0					// Upper bound on average hardness


2lp_main()
{
	data(price,hardness);

	first_stor(Plan[0]);
	last_stor(Plan[MONTHS-1][STOR]);

	and(int i=0;i<MONTHS;i++){
		storage_caps(Plan[i][STOR]);
		blend_constraints(Plan[i][PROC]);
	}

	and(int i=1;i<MONTHS;i++)
		link(Plan[i-1][STOR],Plan[i][PURC],
			Plan[i][PROC],Plan[i][STOR]);

	find_revenue(Plan,price,Revenue);
	max: Revenue;

	output(Revenue,Plan);
}

data(double price[][KINDS],double hardness[])
{
	price = {		
			115, 110, 130, 120, 110,
			115,  90, 110, 130, 130,
			 95, 100, 130, 140, 110,
			125, 120, 120, 110, 120,
			105, 110, 150, 120, 100,
			135,  80, 140, 100,  90 
	};

	hardness = { 5.0, 4.2, 2.0, 6.1, 8.8 };
}


first_stor(continuous FirstMonth[MODES][KINDS])
{
	and(int j=0;j<KINDS;j++)
		FirstMonth[STOR][j] ==
				INITSTOR - FirstMonth[PROC][j] + 
									FirstMonth[PURC][j];
}


last_stor(continuous LastMonth[KINDS])
{
	and(int j=0;j<KINDS;j++)
		LastMonth[j] == ENDSTOR;
}

storage_caps(continuous Stored[KINDS])
{
	and(int j=0;j<KINDS;j++)
		Stored[j] <= STORCAP;
}


blend_constraints(continuous Oils[KINDS])
{
	sigma(int j=0;j<=A;j++) Oils[j] <= LIMITA;
	sigma(int j=B;j<KINDS;j++) Oils[j] <= LIMITB;
	sigma(int i=0;i<KINDS;i++) hardness[i]*Oils[i] 
			>= LBHARD*sigma(int j=0;j<KINDS;j++) Oils[j];
	sigma(int i=0;i<KINDS;i++) hardness[i]*Oils[i]
			<= UBHARD*sigma(int j=0;j<KINDS;j++) Oils[j];
}


link(continuous OldSt[KINDS],Purc[KINDS],
								Proc[KINDS],NewSt[KINDS])
{
	and(int k=0;k<KINDS;k++)
		innerlink(OldSt[k],Purc[k],Proc[k],NewSt[k]);
}

innerlink(continuous OldSt,Purc,Proc,NewSt)
{
	OldSt + Purc == Proc + NewSt;   
}


find_revenue(continuous Plan[MONTHS][MODES][KINDS],
		double price[MONTHS][KINDS], continuous Revenue)
{
	Revenue ==
			sigma(int i=0;i<MONTHS;i++)
				sigma(int j=0;j<KINDS;j++)
					( VATREV*Plan[i][PROC][j] - 
			  			price[i][j]*Plan[i][PURC][j] - 
			  					STORCOST*Plan[i][STOR][j] );
}


output (continuous  Revenue, Plan[MONTHS][MODES][KINDS])
{
string months[MONTHS],modes[MODES],kinds[KINDS];													

	months = {"Jan","Feb","Mar","Apr","May","June"};
	kinds = {"Corn","Peanut","Safflower","Sesame","Sunflower"};
	modes = {"Buy","Process","Store"};

	printf("Maximum revenue is %.2f\n",Revenue);

	and(int m=0;m<MONTHS;m++) {
		printf("\nIn the month of %s\n",months[m]);
		and(int k=0;k<KINDS;k++) {
			printf(" %s oil: ",kinds[k]);
			and(int t=0;t<MODES;t++)
				printf(" %s %.0f vats.\t",modes[t],Plan[m][t][k]);
			printf("\n");
		}
		if  m == 0; then
		printf("Make a sale of %.0f vats.\n",
			sigma(int k=0;k<KINDS;k++) 
			 (INITSTOR+Plan[m][PURC][k]-Plan[m][STOR][k]));
		else
		printf("Make a sale of %.0f vats.\n",
			sigma(int k=0;k<KINDS;k++) 
			 (Plan[m-1][STOR][k]
				+ Plan[m][PURC][k] - Plan[m][STOR][k]));
	}
}
 