Romans Food Market, located in Saratoga, New York, carries avariety of specialty foods from around the world. Two of thestore’s leading products use the Romans Food Market name: RomansRegular Coffee and Romans DeCaf Coffee. These coffees are blends ofBrazilian Natural and Colombian Mild coffee beans, which arepurchased from a distributor located in New York City. BecauseRomans purchases large quantities, the coffee beans may bepurchased on an as-needed basis for a price 10% higher than themarket price the distributor pays for the beans. The current marketprice is $0.47 per pound for Brazilian Natural and $0.62 per poundfor Colombian Mild. The compositions of each coffee blend are asfollows:
| Blend |
|---|
| Bean | Regular | DeCaf |
|---|
| Brazilian Natural | 75% | 40% |
| Colombian Mild | 25% | 60% |
Romans sells the Regular blend for $3.60 per pound and the DeCafblend for $4.40 per pound. Romans would like to place an order forthe Brazilian and Colombian coffee beans that will enable theproduction of 1000 pounds of Romans Regular coffee and 500 poundsof Romans DeCaf coffee. The production cost is $0.80 per pound forthe Regular blend. Because of the extra steps required to produceDeCaf, the production cost for the DeCaf blend is $1.05 per pound.Packaging costs for both products are $0.25 per pound. Formulate alinear programming model that can be used to determine the poundsof Brazilian Natural and Colombian Mild that will maximize thetotal contribution to profit.
| Let | BR = pounds of Brazilian beans purchased to produceRegular |
| BD = pounds of Brazilian beans purchased to produce DeCaf |
| CR = pounds of Colombian beans purchased to produceRegular |
| CD = pounds of Colombian beans purchased to produce DeCaf |
If required, round your answers to three decimal places. Forsubtractive or negative numbers use a minus sign even if there is aplus sign before the blank. (Example: -300)
| Max | BR | + | BD | + | CR | + | CD | | |
| s.t. | | | | | | | | | |
| Regular blend | BR | | | + | CR | | | = | |
| DeCaf blend | | | BD | | | + | CD | = | |
| Regular production | BR | | | | CR | | | = | |
| DeCaf production | | | BD | | | + | CD | = | |
| BR, BD, CR, CD ≥ 0 |
What is the optimal solution and what is the contribution toprofit? If required, round your answer to the nearest wholenumber.
Optimal solution:
If required, round your answer to the nearest cent.
Value of the optimal solution = $Â Â
