Question

Question 13 Using a computerized Inventory Management System, a Paint Supply Store franchise continuously monitors the inventory of all the paint located at each of their 15 stores X and their distribution warehouse. The Paint Supply Store franchise sells an average of 74 gallons of Purple Paint every week (for 52 weeks per year, Standard Deviation of the Demand - 8 gallons). They purchase Purple Paint from their supplier at a price of $4.00 per gallon. It takes 2.50 weeks to receive an order from the supplier. Administrative costs for Ordering paint have been estimated to be $35 per order. Holding Costs - 40% of the purchase price per gallon per year. How much Safety Stock should the company hold to have a Service Level of 99.0M? Reorder Point, ROP = L +SS Service Level Value 99.99% 3.719 dAverage Demand Rate per Time Period 99.90% 3.090 D = Demand Rate per Year 99.00% 2.326 95.00% L-Average Lead time time periods) 1.645 90.00% 1.282 SS = Safety Stock = z dal 85.00% 1.036 80.00% 0.842 dal (Assuming Lead Time is constant as in Periodic review) 0 Standard Deviation of the demand z Number of Standard deviations corresponding to a service level Q = Order Quantity Average Inventory Level=0/2 + SS H = Holding Cost Per Year Per Unit s - Ordering/Setup Cost Per Order Total Annual Inventory Cost = H+ s +H(SS) Time Between 2DS Economic Order Quantity, EOQ = VH EOQ Orders = TBO = Selected Answer: C. 395 gallons of paint Correct Answer: D. 29 gallons of paint
can you show how to do this work

Answer 1

Answer 13:

d = Average Demand rate per time period	74	gallons per week
σ = Standard Deviation	8	gallons
L = Performance cycle, another term for total lead time	2.5	week
z for 99% target service level	2.326
T = time increment used for calculating standard deviation of demand	1	week

Safety stock =	z*(√L/T)*σ
Safety stock = z*(√L/T)*σ = (2.329)*(√2.5/1)*8 = 29.4 ≈	29	gallons