An e$-$commerce retailer sells product A in the local market. He purchases product A directly from the manufacturer located in Italy. The manufacturer charges typically $20$ euros per unit ordered. The manufacturer sends the quantity ordered by truck to a port south of Italy and for that charges the retailer $5$ euros per unit. At this point the retailer contracts a shipping company to transport the order up to a local warehouse in Beirut. The shipping company charges a fixed $400$USD per order that covers all costs from the port of Italy until the local warehouse, except for the customs. It also guarantees a lead time of $10$ days. The customs charges are $10\%$ of the value of the order. Finally, the warehouse charges $$12$ to hold each unit. $(1$Euro $=1\mathrm{.}3$USD $1$ year $=240$ days$)$ The demand for product A is expected to be equal to $18000$ units per year. Product A is a non$-$ perishable and non$-$seasonal product. a$)(5$ points$)$ What is the total unit costs per year incurred by the retailer to sell product A $($not including holding or ordering costs$)?$ b$)(5$ points$)$ What is the optimal quantity to order? c$)(5$ points$)$ Conclude on the total holding costs and total ordering costs per year? The retailer has convinced the shipping company to reduce the fixed charges. We are not told the new charges. However, we know the new "optimal" quantity the retailer will be ordering which is $774$units. a$)(5$ points$)$ Explain quantitatively and qualitatively why it makes sense that the new quantity is smaller than the previous one? b$)(5$ points$)$ in this case, what is the total inventory costs $($holding and ordering$)$ per year? c$)(5$ points$)$ The shipping company agreed to reduce its charges under the condition to increase its lead time from $10$ to $20$ days. What is the financial impact of this increase on the retailer? Demand of product A is of course volatile and its volatility is measured through a daily standard deviation of s $=75$ units. Please use the original data of the problem introduced. The service level of the retailer is $95\%$ which is equivalent to a Z score of Z$\_95\%=1\mathrm{.}645.$ a$)(5$ points$)$ in this setting, what is the financial impact of the lead time on the retailer? To answer this suppose the lead time is $10$ days first and explain the impact if the lead time increases to $20$ days.