A firm wishes to maximize its weekly revenue by producing cast$-$iron products A and $B,$ that require three basic operations: casting, grinding, and drilling. Available time is $36,000$ minutes per week for casting, $2250$ minutes for grinding, and $3600$ minutes for drilling. Each unit of Product A requires $80$ minutes of casting, $2\mathrm{.}5$ minutes of grinding and $9$ minutes of drilling and provides $$4$ of revenue. Each unit of Product B requires $60$ minutes of casting, $4\mathrm{.}5$ minutes of grinding and $4$ minutes of drilling and provides $$2$ of revenue. Formulate an LP to help determine how many of each product that should be manufactured each week?