The Petro Company uses a highly toxic chemical in one of its manufacturing processes. It must have the product delivered by special cargo trucks designed for sage shipment of chemicals. As such, the ordering (and delivery) costs are $200 per order. The chemical product is packaged in 1 gallon containers where each 1 gallon container costs $50 and Petro Company uses 50,000 units over the course of a quarter (where a quarter is 3 months). Each unit costs 10% of the value of the item to hold in inventory per year. Petro is open 200 days out of the year and every order has a 5 day lead time. Please use this information to answer the questions below.

How many 1 gallon containers should Petro order each time they place an order with the supplier if they want to minimize total costs?

Given this order quantity, what is Petro’s TOTAL cost per year (including purchase, order and holding cost)? And which part of this is spent only on holding inventory?

Given an annual demand and the optimal quantity found in part a., how many times a year does Petro place an order?

At what level of inventory will Petro place its next order? Please fully explain how this inventory level breaks down for full credit.