Rainbow Paint Store uses a continuous review inventory system to control its stock levels. For a popular pink paint, historical data shows that the distribution of monthly demand is approximately normal, with a mean of 28 cans and a standard deviation of 8 cans. The replenishment time for this paint is about 14 weeks. Each can of paint costs the store 5 dollars. The order cost is $20 per order and the maintenance costs are based at an annual interest rate of 25%. Management has proposed a type I service level [in-stock rate ()] of 90%. The company operates 52 weeks a year. The manager has asked you to determine the policy adequate inventory. a) (0.5pts) Establish the inventory policy: (how much, when, security inventory, level of service ( and ), and costs) b) (1pts) The manager of Rainbow Paint Store has determined that the unit cost for shortages it is 12 dollars. With this new information, what should the inventory policy then be? (how much, when, safety stock, service level ( and ), and costs)? c) (1.5pts) The procurement manager of Rainbow Paint Store realizes that the initial estimate is considering the steady delivery time, however, the time is normally distributed with a mean of 12 weeks with a variance of 4.5. Considering the cost of scarcity of point b), the information of the demand, and the variability of the time of provisioning, set the new inventory policy (how much, when, inventory of security, level of service ( and ), and costs) d) (2pts) Assume the same information from point c) What would the new inventory policy be like if the manager changes to a periodic review system, which inventory system would you recommend and why?