The Sun Up Convenience Store is open 365 days a year. Sun Up sells 25 bottles of Electric Energy Drink each day. It costs \($8.00\) for Sun Up to order Electric Energy Drink, regardless of the size of the order. The distributor of Electric Energy Drink sells Electric Energy to Sun Up for \($0.25\) a bottle, and the distributor delivers Electric Energy exactly 3 days after Sun Up places an order. If Sun Up were to hold one bottle of Electric Energy Drink in inventory for 1 year, it would cost Sun Up four times (or 400% of) the bottle's cost.

a. What order size will minimize Sun Up's costs? What is the total cost of this order size?

b. Using the order size that minimizes Sun Up's total costs, how many bottles of Electric Energy Drink, on average, will be in inventory?

c. Using the minimum cost order size, how frequently will Sun Up order Electric Energy Drink?

d. When should Sun Up order Electric Energy Drink?

e. Now suppose that the Electric Energy Drink distributor has just made Sun Up an offer: if Sun Up orders at least 1,000 bottles at a time, then the distributor will charge only \($0.22\) for each bottle. What should Sun Up do now?