Suppose that a large software company, Software Monopoly, or SM, is about to release a new software product called Doors, affectionately known as SM-Doors. The software for Doors is estimated to have...

Suppose that a large software company, Software Monopoly, or SM, is about to release a new software product called Doors, affectionately known as SM-Doors. The software for Doors is estimated to have 1,000,000 security flaws. It is also estimated that each security flaw that remains in the software upon release will cost SM about $20, due to lost sales resulting from damage to its reputation. SM pays its developers $100 per hour during the alpha testing phase, and at this phase, developers find flaws at a rate of about 1 flaw for every 10 hours of testing. In effect, customers act as beta testers when they find additional flaws in Doors. Suppose that SM charges $500 per copy of Doors and the estimated market for Doors is about 2,000,000 units. What is the optimal amount of alpha testing for SM to conduct?