Dafoe, The Lone Entrepreneur is a very ambitious man. He wants to make $1000 in the shortest amount of time! He starts out with $0 but is currently receiving $5 per day and he can purchase the following shops at any given time:

1-Shack. Cost: $10 Income: $5/day
2-Mall. Cost $25 Income $15/day
3-Shopping Center. Cost $150 Income $150/day

The money is always paid in at night and Dafoe can purchase as many new shops as his money allows in the mornings.

What would be the best sequence of shops to be purchased to to have a balance of $1000 on hand?

How many days would that take?

Money spent comes out of his balance and so is no longer part of the needed total balance of $1000.

Why is it that your computer solutions have not reproduced the best solution so far achievable by hand?

Even the latest one that optimizes post-1000 yield is not as good as one I can come up with by hand (where on day 13 he has $1920):

Day2: Buy 1 shack
Day3: Buy 1 shack
Day4: Buy 1 shack
Day5: Buy 1 mall
Day6: Buy 1 mall, 1 shack
Day7: Buy 2 malls
Day8: Buy 2 malls, 1 shack (you build 1 mall, 3 shacks)
Day9: Buy 1 Shopping Center
Day10: Buy 1 Shopping Center, 4 Malls (here is where I diverge from Jyqm's solution that gets 980 on day 12)
Day11: Buy 3 shopping centers, 2 Malls
Day12: Buy nothing (or as many shopping centers as you would like)
Total on day 13 = 1920.

One thought I had is: is Dafoe allowed to sell back a building? If so, then we can easily get the required $1000 cash by day 12, especially since we can purchase our first shopping center a full day earlier.

Edited on January 31, 2006, 3:20 pm

Posted by Avin on 2006-01-31 15:17:10