You and your roommates eat a lot of dried ramen noodles. As a group, you eat a case of them every day for the 365 days of the year. You see that Walmart sells them for $4 per case, but it will cost you $2 per trip to get there, so your roommates suggest loading up on extras each trip. But you took OR and remember inventory theory; so you are going to formally determine if that is a good idea. You also expect that any money you tie up in ramen could be earning you 20% per year in the inflationary market - this is the only holding cost you consider for stocking up on ramen.

(a) Figure out the optimal quantity to purchase at each trip and how often to make a trip.

(b) Fortunately, you found a distributor to give you a quantity discount, but they are up in Pawtucket. Considering the travel distance, you estimate it costs you $5 to make the trip to pick them up. However, the discount is that they only charge you $3.80 a case if you buy at least 50. Does it make sense to go to Pawtucket to get them? If so, how often should you go, and how many should you buy during each trip?