Paula Williams is currently completing the design for a drive-in movie theater in Big Flats, New York. She has purchased the land and is now attempting to determine the number of automobiles to accommodate. Each automobile location requires installing a speaker system at a total cost of $250 per location. From her experience with five other drive-ins she has been operating for eight years, Paula estimates that the nightly attendance will range from 100 to 500 automobiles with the relative frequencies given here.

Approximate Number of Automobiles Relative Frequency

100 ............................................................................ 0.10

200 ............................................................................ 0.25

300 ............................................................................ 0.40

400 ............................................................................ 0.15

500 ............................................................................ 0.10

a. In the 20 days of simulated operations, how many daily demands of 300 would you have expected? Did you observe this many in your simulation? Should you have? Explain.

b. After personnel and other operating costs, Paula's average profit is $1 per car. Using your 20 days of simulated data, what is the average nightly profit for the capacities of 300, 400, and 500? How many days of operation will it take Paula to recover the speaker installation cost if all profits are allocated to this cost?