$3\mathrm{.}22($EPQ for Laundry$)$ A restaurant uses $80$ cloth napkins per hour. The napkins are washed by hand at a rate of $110$ per hour. Each time the laundry process is started, the restaurant incurs a fixed cost of $$4\mathrm{.}00.$ Napkins in inventory incur a holding cost of $$0\mathrm{.}08$ per napkin per hour. Stockouts are not allowed. How many napkins should the restaurant have in circulation?

$3\mathrm{.}27($Wagner$-$Whitin for Aircraft Engines$)$ The Pratt & Whitin Company, which manufactures aircraft engines, needs to decide how many units of a particular bolt to order in order to build engines over the next $4$ months. Orders for engines are placed over a year in advance, so the company knows its near$-$term demand exactly; in particular, the number of engines to produce in the next $4$ months will be $150,100,80,$ and $200$ in months $1$ through $4,$ respectively. Each engine requires a single bolt. Orders for bolts incur a fixed cost of $$120,$ and bolts held in inventory incur a holding cost of $$0\mathrm{.}80$ per bolt per month. Find the optimal order quantities in each period and the optimal total cost.