Question:

Romans food market carries a variety of specialty foods from around the world. Two of the stor’s leading products use the Romans Food Market name: Romans Regular Coffee, and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Columbian Mild Coffee beans, which are purchased from a distributor. Because Romans purchases large quantities, the coffee beans may be purchased on as as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound of Brazilian Natural and $0.62 per pound for Columbian Mild. The compositions of each coffee blend are as follows:

Romans sells the Regular Blend for $3.60 per pound and DeCaf blend for $4.40 per pound. Romans would like to place an order for the Brazilian and Columbian coffee beans that will enable the production of 1000 pounds of Romans Regular Coffee and 500 pounds of Romans DeCaf coffee. The production cost is $0.80 per pound for the regular blend and $1.05 per pound for DeCaf blend. 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 Columbian Mild that will maximize the total contribution to profit. What is the optimal solution and what is the contribution to profit?