Opening a multimillion dollar musical on Broadway is the ultimate financial gamble. Hits such as The Phantom of the Opera can earn millions in profit. Disasters too numerous to name have meant millions in losses. In the 2011 season, the producers of the musical Spider Man, Turn off the Dark with state-of-the-art special effects and music and lyrics by Bono and The Edge faced high hopes and an important decision: whether to mount the usual series of out-of-town previews or to open directly on Broadway. A direct opening would save considerable costs (estimates for the Broadway run alone were spiraling above $60 million) but would give up the valuable opportunity to revise and craft the show based on audience reactions in tryouts.

a. A direct Broadway opening is projected to have three possible outcomes: a "Hit" (implying net profit of $30 million), a "Solid Show" ($10 million in profit), or a "Bomb" ($50 million in losses). The producers' best probability estimates of these outcomes are .3,
.5, and .2, respectively.

What is the expected profit of a direct Broadway opening?

b. Alternatively, the producers could test the production in a series of out-of-town previews at an added cost of $7 million. By carefully taking the pulse of the audience, the producers can expect one of three findings. If the show is "Well-Received" (probability .35), then only mild tweaking will be needed and estimated Broadways profits from an extended run will be $24 million. If the show has definite "Kinks" (probability .45), then besides being less appealing to audiences, the show will require fixing and reworking, reducing the estimated Broadway profit to $12 million. Finally, if the production turns out to have "Major Problems" in front of the preview audiences (probability .2), then the producers should cut their losses and not open on Broadway at all (so they are only $7 million in the red).

What is the expected overall profit from previewing the show out of town? Is this more profitable than opening on Broadway directly?