While traveling around Peru, you met the owner of Nomads, one of the biggest tourism companies in the city of Cusco. Ms. James hired you to help Nomads with food inventory management for their best-seller tourism circuit: the 4-days Inca Trail hiking to Machu Picchu. Talking with Matthew, the operations manager, you learn that tour packages include specific items in their cost but that also travelers can buy additional products - like organic yogurts- along the journey. For the 4-days Inca Trail Hiking, theres a special issue adding complexity to the inventory management team. Once the tour leaves the city, it cant get additional units of the organic yogurts for the journey. Also, based on the perishability of this product, Nomads will discard anything thats not sold during the tour. Considering that Nomads is working mainly with international clients, all its prices and costs are set in US Dollars. The selling price of this product is $20 per unit, and it costs the company $5.36 to buy them.

You also know that the demand for organic yogurts per 4-days tour follows a normal distribution with a mean of 119 and a standard deviation of 12. What is the optimal order quantity of organic yogurts that would maximize the tour sales profit?

How many units short would the company be on the next 4-days tour if ordering 90 units instead?

You are not comfortable with the expected outcomes of Question 1 and Question 2, so you decide to evaluate an alternative approach. What should be the order quantity if Ms. James wants the probability of running out of stock during the 4-days tour to be lower than 10%?

Ms. James disregards this last option as well, and asks the team to brainstorm on other profit improvement opportunities. Matthew, suggests selling the products at a salvage value of $3.06 at the end of the tour, to avoid going back with the unsold units to the city just to discard them.

What would be the optimal order quantity under this suggested scenario? What would be the company's expected profit if you decide to order this quantity?