Brazilian Natural Columbian Mild

BR = pounds of Brazilian regular blended beans

BD = pounds of Brazilian DeCaf beans

CR = pounds of Colombian regular beans

CD = pounds of Colombian DeCaf beans

Bean prices

Brazilian

1.10(0.47) = 0.517 per pound

Colombian

1.10(0.62) = 0.682 per pound

total revenue = 4.40(BD + CD) + 3.60(BR + CR)

Sum of beans = 0.682(CR + CD + 0.517(BR + BD)

production cost = 0.80(BR + CR) + 1.05(BD + CD)

distributing cost = 0.25(BR + CR) + 0.25(BD + CD)

Total contribution to profit = 2.033BR + 2.583BD + 1.868CR + 2.418CD

Regular percent blend

BR = 0.75(BR + CR)

0.25BR - 0.75CR = 0

DeCaf percent blend

BD = 0.40(BD + CD)

0.60BD - 0.40CD = 0

Pounds of Regular: BR + CR = 1000

Pounds of DeCaf: BD + CD = 500

Max 2.033BR+2.583BD+1.868CR+2.418CD

s.t.

0.25BR-0.75CR =0

0.60BD-0.40CD =0

BR+CR= 1000

BD+CD= 500

BR, BD, CR, CD ?0

The optimal solution is BR = 750, BD = 200, CR = 250, and CD = 300.

The