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 $1,100$ pounds of Romans Regular coffee and $600$ 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 $.)$