#define FUND 55000.0
#define AA 10				// number of AA bonds
#define AAA 5				// number of AAA bonds
#define PPH 0				// price per hundred
#define RR 1 				// rate of return
#define LIMIT 7500.0

double dbla[2][AA];						// data from Table 9.1
double trpla[2][AAA];					// data from Table 9.2

continuous DblA[AA],TrplA[AAA],Mm,Return;
continuous TotalAA,TotalAAA;				// auxiliary variables 

int sortAA[AA], sortAAA[AAA];

data() { 

	dbla = { 
		421, 686, 375, 330, 400, 444, 522, 545, 550, 275,
		.09,.084,.0825,.081,.0825,.081,.091,.09,.083,.0825
	};

	trpla = { 
		782, 982, 466, 700, 700,
		.076, .075, .07, .0775, .08
	};
}

setup()
{
	TotalAA == sigma(int i=0;i<AA;i++)
						dbla[PPH][i]*DblA[i];

	TotalAAA == sigma(int j=0;j<AAA;j++)
						trpla[PPH][j]*TrplA[j];
 
	TotalAA + TotalAAA + Mm == FUND;
	
	Mm >= .12*TotalAA;
     
	Mm >= .20*TotalAAA;
 
	.85*TotalAAA >= TotalAA;
	
	Return ==
		sigma(int i=0;i<AA;i++)
                    dbla[RR][i]*dbla[PPH][i]*DblA[i] +
		sigma(int j=0;j<AAA;j++)
                    trpla[RR][j]*trpla[PPH][j]*TrplA[j] +
		.025*Mm;

	Return >= .065*FUND;						// client’s requirement
}

bounds()
{
	sharp_bounds(AA,dbla[PPH],DblA);				// tightens model
	sharp_bounds(AAA,trpla[PPH],TrplA);  
}

sharp_bounds(int a, double price[], continuous Bonds[]) 
{
	and(int i=0;i<a;i++) 
		Bonds[i] <= floor(LIMIT/price[i]);
}

fix_security(continuous Security)
{
	max: Return;
	Security == floor(Security);				// Progressive roundoff
}

try(continuous Bond)
{
int bottom, top;

	min: Bond;
	bottom = ceil(Bond);					// Lower bound for loop

	max: Bond;
	top = floor(Bond);						// Upper bound for loop
	
	//Bond==top,...,Bond==k+1 do not lead to a solution
	or(int k=top;k>=bottom;k--) //If k==bottom-1, backtrack
		Bond == k;			// Purchase bonds; return to and loop
}

new_central_loop()
{
	and(int i=0;i<AA;i++) 
		try(DblA[sortAA[i]]);
	and(int j=0;j<AAA;j++) 
		try(TrplA[sortAAA[j]]);
}

arrange(int a,sort[], double rr[])
{
int temp;

	and(int k=0;k<a;k++)
		sort[k] = k;

	and(int i=a-1;i>=0;i--) 
		and(int j=0;j<i;j++)
			if rr[sort[j]] < rr[sort[j+1]];
			then {
			       temp = sort[j];
			       sort[j] = sort[j+1];
			       sort[j+1] = temp;
			}
}

output()
{
	printf("Place %.2f in AA Bonds. \n",TotalAA);
	printf("Place %.2f in AAA Bonds. \n",TotalAAA);
	printf("Place %.2f in Money Market funds. \n",Mm);
	printf("Rate of return is %.5f. \n",Return/FUND);
}

2lp_main()
{
	data();
	setup();
	bounds();
	
	arrange(AA,sortAA,dbla[RR]);
	arrange(AAA,sortAAA,trpla[RR]);

	new_central_loop();

	output();
}

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