Suppose that Dr. Su really wants to get out of academia for more money but becoming a Youtuber may not be the best option. He decides to start a new wholesale business and now sells high-end specialized electronics to a retailer called TX Corp. TX purchases each unit from Dr. Su for $75 and retails them for $130. Dr. Su's sourcing cost from a mysterious supplier is $35. At the end of the season, TX estimates the salvage value is only about $25 for each unit. TX believes this season's demand can be represented by a normal distribution with amean of 250 and a standard deviation of 100.

The following is the supply chain:

Mysterious supplier--> Dr. Su Wholesale--> TX Corp. Retail --> customers

(a) What is TX's optimal order quantity?

(b) What is Dr. Su's profit when TX orders at its optimal quantity?

(c) From a maximize-your-own-profit perspective, should TX order at a different amount than (a)? state your reason.

(d) TX discovers a new after-season market that they can sell at a higher price of ($50) but needs to spend an extra $5 per unit of shipping costs and $5 per unit for holding. What quantity should TX order?

---assume that TX does not have the new market option in (d) for the following questions---

(e) Consider Dr. Su's store and TX retail store as a single entity (vertical integration), what is the optimal order quantity for the single entity?

(f) If Dr. Su wants to encourage TX to order close to or more than the amount in (e) using a buyback contract, will a buyback price = $70 works?

(g) Dr. Su decides to use a revenue-sharing contract and lower the price from $75 to $30 but asks TX to share a fraction of its revenue. They both agree on the revenue share fraction of 40% (f = 0.4). With the revenue-sharing clause, how many should TX order from Dr. Su?