Total Supplies is a first class retail chain that has a store in the Savanna La Mar area. The companys main product is its high-end phones, among which is the JPhone 14 pro max. The company orders 15 Torch (Q) from their supplier when their inventory reaches 5 units (R). Daily demand for JPhone varies according to the probability distribution shown below. The lead time is zero since orders made are received the next day in time for sale. The cost to hold one unit in inventory for one day is $0.50. The cost to place an order to replenish their inventory is $100. Stock-out costs per unit are $40. Initial inventory is 15 units.

Daily Demand (units)Probability00.0510.0520.2030.3040.3050.10

1. Calculate Quest Worlds expected Daily Demand using the probability distribution given.

1. Construct the appropriate random number mapping for the random variable.

Daily Demand (units)ProbabilityF(x)RN mapping00.05 10.05 20.20 30.30 40.30 50.10

1. Simulate 8 days by using the random numbers given below and complete the given activity table.

Random Numbers To Be Used in the SimulationDay12345678Demand0.570.590.840.190.820.900.020.11

Activity Table

DayDaily DemandClosing InventoryOrdersStock OutHolding CostOrder CostStock-Out CostTotal Daily Cost1 2 3 4 5 6 7 8

1. What is the average daily cost to manage this inventory policy?
2. Discuss the advantages and disadvantages of simulation