EG electric sells two types of laptops (type A and type B). Both types of laptops are manufactured in Bangladesh and will be shipped to the distribution center of EG electricin U.S. The lead time is three weeks. The two types of laptops share a common body. The only difference between them is the battery.Type A laptop is equipped with the battery A that can work in extreme cold weather. Type B laptop is equipped with the battery B that can work in extreme hot weather. The weekly demand of type A laptop follows normal distribution with mean of 200 and variance of 11.The weekly demand of type B laptop follows normal distribution with mean of 300 and variance of 12. Assume these two demands are independent. EG electric continuously review its inventory of these two types laptops and will place order following (Q, R) strategy. It wants to achieve the goal that the probability of stock-out during the lead time can be controlled below 10%.

a) What is the safety stock of these two types of laptops that the distribution center of U.S needs to hold?

b) If the postponement strategy is adopted, i.e., the laptop without batteries, and two types of batteries will be shipped to the distribution center in U.S, what is the safety stock for laptop without batteries, and two types of batteries?

c) Suppose the holding cost of the laptop with battery is 3 per unit per week, the holding cost of the laptop without battery(if we adopt postponement strategy) is 2 per unit per week, and the holding cost for the battery (either battery A or battery B)is 0.5 per unit per week. What is the saving of the holding cost of the safety stock per week due to the adoption of postponement strategy?

d) Suppose we do not know the holding cost for the battery(per unit per week), while the other conditions are same as part c), what is the boundary value of this battery holding cost per unit per week such that the adoption of postponement strategy can lead to a reduction of weekly holding cost?

e) If we use the strategy of component commonality, we design a new universal battery that can work in both weather conditions, what will be the safety stock for the laptop? Assume the holding cost for the laptop with universal battery is still 3 per unit per week, what is the saving of the holding cost of the safety stock compared to the original scenario?

f) Suppose that both postponement and component commonality have some technical difficulties for implementation, thus EG electric determines to reduce the lead time for transportation from Bangladesh to U.S. If the lead time can be reduced from three weeks to two weeks, what is the reduction of safety stock?