Develop and solve a linear programming model to maximize contribution to profit. $($Asssume $R_i$ is the amount of ingredient i used in producing regular, and $S_i$ is the amount of ingredient i used in producing Super. Use the units of barrels and dollars for all answers.$)$

Max$2R_1+4\mathrm{.}5R_2+R_3+3\mathrm{.}5S_1+6S_2+2\mathrm{.}5S_3$

s$.$t$.$

Input $1$ Capacity

Input $2$ Capacity

Input $3$ Capacity

Max Demand for Regular

$R_1+R_2+R_{3}430000$

Max Demand for Super

Required Octane Level, Regular

Required Octane Level, Super

$R_1,R_2,R_3,S_1,S_2,S_{3}0$

What is the optimal contribution to profit?

Report your values for $R_1,R_2,R_3,S_1,S_2,S_3.$

$(R_1,R_2,R_3,s_1,s_2,s_3)=(,)$

What is the maximum profit $($in dollars$)?$