Show your work on calculations; "result only" answers will get only half credit even if they are correct, and will not get any partial credit if they are wrong. A restaurant currently uses an average of 180 boxes of napkins per day over the 300 days that it is open in a year (50 weeks a year, 6 days a week). The cost to order napkins from the distributor is $200 per order and the regular purchase price per box is $10. Assume that the restaurant employs a continuous review system with a service level of 91% (z = 1.34), and uses an annual holding cost rate of 21%. The following are also estimated: Standard deviation of daily demand = 25 boxes Average lead time = 4 days Standard deviation of lead time = 1 day a) [25] What is the optimal order quantity for these napkins? b) [10] What is the average time between orders if they use the optimal order quantity? c) [30] What safety stock and reorder point should the restaurant use? d) [35] Calculate the resulting total annual inventory costs, assuming that the restaurant also accounts for the pipeline inventory. e) [BONUS: 25] Suppose the distributor of these napkins offers a quantity discount: For orders between 10,000 and 19,999 boxes, the unit price drops to $9.75 per box; for orders of 20,000 or more boxes, the price drops to $9.60. What order size should the restaurant use, given this offer? EOQ= SS=ZOALT 2DS hP ALT= Q s=-2/22 CS= ROP = D L + SS Lxo + D X OT PS = D L D TC=S=+H(CS+SS+ PS) + PD =s=+

Show your work on calculations; \"result only\" answers will get only half credit even if they are correct, and will not eetany partial credit if they are wrong A restaurant currently uses an average of 180 boxes of napkins per day over the 300 days that it is open in a year ( 50 weeks a year, 6 days a week). The cost to order napkins from the distributor is \\( \\$ 200 \\) per order and the regular purchase price per box is \\( \\$ 10 \\). Assume that the restaurant employs a continuous review system with a service level of \91, and uses an annual holding cost rate of \21. The following are also estimated: Standard deviation of daily demand \\( =25 \\) boxes Average lead time \\( =4 \\) days Standard deviation of lead time \\( =1 \\) day a) [25] What is the optimal order quantity for these napkins? b) [10] What is the average time between orders if they use the optimal order quantity? c) [30] What safety stock and reorder point should the restaurant use? d) [35] Calculate the resulting total annual inventory costs, assuming that the restaurant also accounts for the pipeline inventory. [BONUS: 25] Suppose the distributor of these napkins offers a quantity discount: For orders between 10,000 and 19,999 boxes, the unit price drops to \\( \\$ 9.75 \\) per box; for orders of 20,000 or more boxes, the price drops to \\( \\$ 9.60 \\). What order size should the restaurant use, given this offer? \\[ \\begin{array}{c} E O Q=\\sqrt{\\frac{2 D S}{h P}} \\quad R O P=D L+S S \\\\ S S=Z \\sigma_{d L T} \\quad \\sigma_{d L T}=\\sqrt{L \\times \\sigma_{d}^{2}+D^{2} \\times \\sigma_{L T}^{2}} \\\\ C S=\\frac{Q}{2} \\quad P S=D L \\\\ T C=S \\frac{D}{Q}+H(C S+S S+P S)+P D \\end{array} \\]