1. A shophas a demand for water is approximated by a normal distributionwith a mean of 31 gallons per week and a standard deviation of 4gallons per week. The manager desires a service level of 90percent. The lead time is three days, and the shop opens seven daysa week. (9 marks)
a. If an ROP model is used, what ROP would be consistent with thedesired service level?
b. If a fixed-interval model is used, how much should be orderedfor the 90 percent service level with anorder interval of 7 days and a supply of 10 gallons on handat the order time?
c. Suppose the manager is using the ROP model described in parta. One day after placing an order with thesupplier, the manager receives a call from the supplier that theorder will be delayed because of problemsat the supplier’s plant. The supplier promises to have theorder there in two days. After hanging up,the manager checks the water and finds that 7 gallons have beenused since the order was placed. Assuming the supplier’spromise is valid, what is the probability thatwater will run out before the shipmentarrives? (calculate to 2 decimal places)