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 $\backslash (10\backslash \%\backslash )$ higher than the market price the distributor pays for the beans. The current market price is $\backslash (\backslash$$ $0\mathrm{.}47\backslash )$ per pound for Brazilian Natural and $\backslash (\backslash$$ $0\mathrm{.}62\backslash )$ per pound for Colombian Mild. The compositions of each coffee blend are as follows:

Romans sells the Regular blend for $\backslash (\backslash$$ $3\mathrm{.}60\backslash )$ per pound and the DeCaf blend for $\backslash (\backslash$$ $4\mathrm{.}40\backslash )$ per pound. Romans would like to place an order for the Brazilian and Colombian 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 $\backslash (\backslash$$ $0\mathrm{.}80\backslash )$ per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $\backslash (\backslash$$ $1\mathrm{.}05\backslash )$ per pound. Packaging costs for both products are $\backslash (\backslash$$ $0\mathrm{.}25\backslash )$ per pound.

Formulate a linear programming model $($identify and define decision variables, objective function, and constraints$)$ that can be used to determine the amount $($in pounds$)$ of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. For "Part A$"$ you do NOT need to solve this problem using Excel, you just need to do the LP formulation in the standard mathematical format.

Part b $($bonus worth $20$ pts$)$: Solve the LP problem that you formulated in "Part a$"$ using Excel. Give the values of each decision variable and the objective function. You MUST attach a copy of the solution report.

LOOK AT PICTURE FOR FULL PROBLEM