Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most $20,000$ gallons.

produced in order to maximize total profit contribution. $($Let $R$ be the gallons of regular gasoline and let $P$ be the gallons of premium gasoline.$)$

Max

s$.$t$.$

Grade A crude oil available

Production capacity

Demand for premium

$R,P0$

$($b$)$ What is the optimal solution?

$R=$

$P=$

profit $=$$

$($c$)$ What is the value of the slack variable in the Grade A crude oil constraint?