An automobile manufacturer uses an import component for the assembly of a lightweight commercial vehicle with an annual demand of A units.

Each import cycle costs B money units and each component costs C money units. The finance manager reports that the unit annual inventory holding cost is D % of the unit cost.

The length of the import cycle (lead time) fits a normal distribution with an average of E days and a standard deviation of F days. The daily component demand of the assembly line also fits a normal distribution with an average of G units and a standard deviation of H units. The distributions of lead time and daily demand are independent.

The unavailability of the component stops the assembly line which causes a loss of I times the unit cost of the component.

1. Compute the lot size of the components to be imported each time and the amount of the safety stock that minimizes total annual inventory-relat costs.
2. Calculate total annual inventory -related costs paying attention to the categories of ordering, inventory holding, and stock-outs.