Yes, I'm still alive. Thanks for asking. Life has been a bit busy, and considering that the readership of this site seems to consist of Joe Cantore, there's not a lot of incentive for me to post here.

But anyway.... Here's a puzzle for you. It's set in the mythical country of Libertaria. Commerce there only follows one rule, that markets must be free and open. Sellers can set whatever price they want to for their goods and/or services, but must then sell to anyone who meets that price; they may not set different prices depending on the customer. It's possible to get credit in Libertaria, but limits are set based on what the individual could reasonably be expected to pay back.

One not-very-fine day, the ship S. S. Libertaria goes down. Naturally, the ship's lifeboats have long ago been bought by speculators who want to maximize their profits, and they'll set optimum prices accordingly.

For purposes of the puzzle, let's suppose that the following people are on the boat:
  • Jonas Grumby, ship's captain. Credit limit: $75,000; ships captains in Libertaria don't get paid much but he does have a Navy pension to borrow against.
  • William Gilligan, ship's first mate. Credit limit: $35,000; he has no savings to speak of but is young and in good health.
  • Thurston Howell III, investment banker, and Mrs. Howell, wife. Credit limit: $1,000,000 between the two of them.
  • Ginger Grant, actress. Credit limit: $300,000.
  • Roy Hinkley, scientist. Credit limit: $50,000.
  • Mary Ann Summers, farmer's daughter. Credit limit: zero. Dad's farm isn't doing at all well this year.

Assuming the lifeboats have enough space to be able to transport any or all of these people, what price is optimal for the lifeboat owners to set? For advanced solving, add a non-fixed cost of $10 per passenger for later cleaning of the lifeboat.