Problem 9-13 (Algorithmic)

Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store’s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 11% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows:

Blend
Bean Regular DeCaf
Brazilian Natural 75% 35%
Colombian Mild 25% 65%
Romans sells the Regular blend for $3.2 per pound and the DeCaf blend for $4.3 per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of 900 pounds of Romans Regular coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.89 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.09 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit.

Let BR = pounds of Brazilian beans purchased to produce Regular
BD = pounds of Brazilian beans purchased to produce DeCaf
CR = pounds of Colombian beans purchased to produce Regular
CD = pounds of Colombian beans purchased to produce DeCaf
If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

The complete linear program is

Max fill in the blank 1
2.06
BR + fill in the blank 2
2.96
BD + fill in the blank 3
2.06
CR + fill in the blank 4
2.96
CD
s.t.
fill in the blank 5
2.06
BR + fill in the blank 6
2.06
CR = fill in the blank 7
900
fill in the blank 8
2.96
BD + fill in the blank 9
2.96
CD = fill in the blank 10
500
fill in the blank 11
BR fill in the blank 12
CR = fill in the blank 13
fill in the blank 14
BD + fill in the blank 15
CD = fill in the blank 16
BR, BD, CR, CD ≥ 0
What is the contribution to profit?

Optimal solution:

BR = fill in the blank 17
BD = fill in the blank 18
CR = fill in the blank 19
CD = fill in the blank 20
If required, round your answer to two decimal places.

Value of the optimal solution = $ fill in the blank 21