A linear programming computer package is needed.

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{.}47$ per pound for Brazilian Natural

and $$0\mathrm{.}62$ per pound for Colombian Mild. The compositions of each coffee blend are as follows.

Romans sells the Regular blend for $$3\mathrm{.}60$ per pound and the DeCaf blend for $$4\mathrm{.}40$ 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 $400$ pounds of Romans DeCaf coffee. The production cost is

$$0\mathrm{.}80$ per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $$1\mathrm{.}05$ per pound.

Packaging costs for both products are $$0\mathrm{.}25$ per pound.

$($a$)$ 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, and $CD=$ pounds of Colombian beans purchased to produce DeCaf.$)$

Max

s$.$t$.$

Regular $\%$ constraint

DeCaf $\%$ constraint

Pounds of Regular

Pounds of DeCaf

$($b$)$ What is the optimal solution?

$(BR,BD,CR,CD)=(,)$

$($c$)$ What is the contribution to profit $($in $ $)?($Round your answer to two decimal places.$)$

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