Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store$$s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as$-$needed basis for a price $12\%$ higher than the market price the distributor pays for the beans. The current market price is $$0\mathrm{.}45$ per pound for Brazilian Natural and $$0\mathrm{.}67$ per pound for Colombian Mild. The compositions of each coffee blend are as follows:

Blend

Bean Regular DeCaf

Brazilian Natural $60\%40\%$

Colombian Mild $40\%60\%$

Romans sells the Regular blend for $$3\mathrm{.}3$ per pound and the DeCaf blend for $$4\mathrm{.}5$ per pound. Romans would like to place an order for the Brazilian and Colombian coffee beans that will enable the production of $1100$ pounds of Romans Regular coffee and $525$ pounds of Romans DeCaf coffee. The production cost is $$0\mathrm{.}84$ per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $$1\mathrm{.}08$ 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

Max fill in the blank $1$

BR $+$ fill in the blank $2$

BD $+$ fill in the blank $3$

CR $+$ fill in the blank $4$

CD

s$.$t$.$

fill in the blank $5$

BR $+$ fill in the blank $6$

CR $=$ fill in the blank $7$

fill in the blank $8$

BD $+$ fill in the blank $9$

CD $=$ fill in the blank $10$

fill in the blank $11$

BR fill in the blank $12$

CR $=$ fill in the blank $13$

fill in the blank $14$

BD $+$ fill in the blank $15$

CD $=$ fill in the blank $16$

BR$,$ BD$,$ CR$,$ CD $>=0$

What is the contribution to profit?

Optimal solution:

BR $=$ fill in the blank $17$

BD $=$ fill in the blank $18$

CR $=$ fill in the blank $19$

CD $=$ fill in the blank $20$

If required, round your answer to two decimal places.

Value of the optimal solution $=$ $ fill in the blank $21$