Aqua guard manufactures three models of water purifiers in three separate plants at Taiwan. These plants serve the demand in Europe. All three models sell at a unit price of $100 and the holding cost is 5% of the selling price per month. The monthly demand for these models is normally distributed with the following parameters:

Model 1: Mean 1000, SD 300

Model 2: Mean 1000, SD 300

Model 3: Mean 1000, SD 300

The demand for Model 1 and Model 2 has a correlation coefficient of -0.35, while that for Model 3 is independent of the other two models.

Consider Aqua guard’s distribution in Europe. They have a central DC that caters to the European market. The lead time from Taiwan to their DC is 2 months and orders are placed every month. Determine the expected end-of-month inventory for each product when a target in-stock probability is 98%.