ANSWER I AND II $1.$ Sherwin$-$Williams plans to introduce a new paint to the market. As the production planner, you have assembled the following cost data and demand forecast for the upcoming year: Quarter$-1$ Quarter$-2$ Quarter$-3$ Quarter$-41,8001,1001,600900$ COSTS Beginning inventory: $0$ barrel Inventory holding cost $=$ $$40$ per barrel per quarter Stockout cost $=$ $$150$ per barrel Increasing capacity via hiring employees $=$ $$40$ per barrel Decreasing capacity via terminating employees $=$ $$80$ per barrel Subcontracting cost $=$ $$60$ per barrel Production cost $=$ $$30$ per barrel Beginning production capacity $=1,800$ barrels per quarter There is no backlog $($i$.$e$.,$ any unmet demand is lost and cannot be satisfied using future production$).$ Your job is to develop an aggregate plan for the production. Currently, you consider three options: Option A: A chase strategy with hiring and layoffs Option B: A level strategy with a full in$-$house production in which the production rate is set to the average quarter forecast Option C: A level strategy with a constant production of $1,200$ barrels per quarter along with subcontracting $($if needed$).$ i$.$ Develop an aggregate plan for each option $(15$ points$)$ ii$.$ Calculate the total cost $($i$.$e$.,$ production, inventory, hiring$/$layoff$,$ and subcontracting costs$)$ and determine which option Sherwin$-$Williams should choose. $(5$ points$)$