Need assistance with answering a and b.

Aquaguard manufactures three models of water purifiers in three separate plants in Taiwan. These plants serve the demand in Europe. All three models sell at a unit price of $50 and the holding cost is 3% of the selling price per month. The monthly demand for these models is identical and normally distributed with the following parameters: Mean 900, SD 400.

The demand for Model 1 and Model 2 has a correlation coefficient of -0.25, while that for Model 3 is independent of the other two models.

a) Consider Aquaguards distribution in Europe. They have a central DC that caters to the European market. The lead time from Taiwan to their DC is 1 month and orders are placed every other month (i.e., one order per two months). Determine the expected total end-of-month inventory for all three products when the target in-stock probability is 98%, and then calculate the expected total monthly holding cost for all three models. In this part, please assume that ordering decisions are made independently for the three purifiers (i.e., this is NOT a pooling question). [10 pts]

b) Aquaguard has the option of redesigning its products. It can develop a base product B and ship it to the DC. The base product can then be customized into any one of the Models and sold (delayed differentiation). The company chooses to redesign Model 1 and Model 2, while Model 3 remains untouched (i.e., only Models 1 and 2 are pooled into product B). The lead time, the in-stock target level and the ordering policies remain the same. Determine the total expected end-of-period inventory for product B and Model 3 and then calculate the expected total monthly holding cost. How much (and what %) is the holding cost savings (compare your result to that of in part a)? (Hint: This is a pooling question where you will only pool Models 1 and 2, Model 3 will not change) [15 pts]