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$800$pounds of Romans Regular coffee

and$300$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.$)$$$$