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 $10\%$ higher than the market price the distributor pays for the beans. The current market price is $$0\mathrm{.}46$ per pound for Brazilian Natural and $$0\mathrm{.}64$ per pound for

Colombian Mild. The compositions of each coffee blend are as follows:

Romans sells the Regular blend for $$3\mathrm{.}1$ per pound and the DeCaf blend for $$4\mathrm{.}3$ per pound. Romans would like to place an order for the Brazilian and Colombian coffee

beans that will enable the production of $1050$ pounds of Romans Regular coffee and $500$ pounds of Romans DeCaf coffee. The production cost is $$0\mathrm{.}8$ per pound for the

Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $$1\mathrm{.}15$ per pound. Packaging costs for both products are

$$0\mathrm{.}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

What is the contribution to profit?

Optimal solution:

$BR=$

$BD=$

$CR=$

$CD=$

If required, round your answer to two decimal places.

Value of the optimal solution $=$$