Problem 9-13 (Algorithmic)
Romans Food Market,located in Saratoga, New York, carries a variety of specialty foodsfrom around the world. Two of the store’s leading products use theRomans Food Market name: Romans Regular Coffee and Romans DeCafCoffee. These coffees are blends of Brazilian Natural and ColombianMild coffee beans, which are purchased from a distributor locatedin New York City. Because Romans purchases large quantities, thecoffee 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 Naturaland $0.62 per pound for Colombian Mild. The compositions of eachcoffee blend are as follows:
| Blend |
|---|
| Bean | Regular | DeCaf |
|---|
| Brazilian Natural | 75% | 35% |
| Colombian Mild | 25% | 65% |
Romans sells theRegular blend for $3.2 per pound and the DeCaf blend for $4.3 perpound. Romans would like to place an order for the Brazilian andColombian coffee beans that will enable the production of 900pounds of Romans Regular coffee and 500 pounds of Romans DeCafcoffee. The production cost is $0.89 per pound for the Regularblend. Because of the extra steps required to produce DeCaf, theproduction cost for the DeCaf blend is $1.09 per pound. Packagingcosts for both products are $0.25 per pound. Formulate a linearprogramming model that can be used to determine the pounds ofBrazilian Natural and Colombian Mild that will maximize the totalcontribution 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, roundyour answers to three decimal places. For subtractive or negativenumbers use a minus sign even if there is a + sign before theblank. (Example: -300)
The complete linearprogram is
| Max | BR | + | BD | + | CR | + | CD | | |
| s.t. | | | | | | | | | |
| BR | | | + | CR | | | = | |
| | | BD | | | + | CD | = | |
| BR | | | | CR | | | = | |
| | | BD | | | + | CD | = | |
| BR, BD, CR, CD ? 0 |
What is thecontribution to profit?
Optimal solution:
If required, roundyour answer to two decimal places.
Value of the optimalsolution = $
