Mylea delivers customized stockings to the boutique fifty at a time. It takes three hours to make each set of stockings. Forty stockings are sold every hour, and management has decided that $20\%$ of the expected number of stockings in a batch should be on hand as safety stock. How many Kanban card sets are needed? You may presume that a container holds a single batch of stockings.

Jaleel has decided to sell personalized Christmas ornaments. He has three stores who have agreed to carry the ornaments, one in Greensboro $(30,80)$; one in Charlotte $(20,20)$ and one in Raleigh $(80,50).$ Raleigh estimates it will sell $2500$ ornaments a year; Greensboro expects to sell $7500$ ornaments a year and Charlotte expects to sell $6000$ ornaments a year. Use the centroid method to determine where to locate Jaleel's ornament workshop.

If Jaleel decides to drop Raleigh as a location and instead sell in Norfolk $(120,90),$ to where would the centroid method suggest he move his workshop? Presume that he will sell as many in Norfolk as he did in Raleigh.

$13.$ Jaleel expects to sell $20000$ spires. Each ornament weighs $8$ ounces but must be packed in a carton that is $8"x{88}^{\text{'}\text{'}}{16}^{\text{'}\text{'}}$ to avoid breakage. The cost of processing the order is $$100$ per order. Carrying cost is $50\%$ of the cost of the ornaments due to the potential for breakage. Jaleel orders the plain ornaments to be customized from one of two companies: Clearly Glass or Rise and Shine. Clearly Glass charges $$1$ an ornament. Rise and Shine charges $$1\mathrm{.}25$ per ornament. Because the ornaments are bulky but not heavy, the shipping companies charge a flat rate of $$60$ per mile per pallet, with a pallet holding $250.$ If the company is shipping an entire tractor trailer full $(4000$ units or $16$ pallets$),$ because the company can add a fake floor to allow for a second layer, the cost per pallet drops to $$35$ per mile. Rise and Shine is $75$ miles away, Clearly Glass is $90$ miles away. Determine whether it's better for Jaleel to order from Rise and Shine or Clearly Glass and determine whether Jaleel should order by the pallet or by the tractor trailer truck$-$load, showing your calculations.