3. Suppose you are working security at a music event at Petco Park. The maximum capacity is 42445 people. Your job is to count the total number of people who enter and stop when that value gets to 42445. 2 You are given a mechanical "tally counter" (see picture.) A tally counter is a device such that every time you press a button, the value on the counter increments by 1. The value on the counter is displayed using a particular number of wheels, each wheel having 10 digits {0,...,9}. Your supervisor gives you a tally counter with 5 wheels. This is sufficient for your job since this tally counter can display any number between 00000 and 99999. The value 42445 is within this range so it will do the job. (A tally counter with 4 wheels would be insufficient because that can only count up to 9999.) If you change the number of characters on the wheel, then you may need more or fewer wheels for the job. For example, 5 wheels is insufficient if each wheel has 8 characters {1,...,7} and the value is displayed in base 8. The reason it is insufficient is because it can only display numbers in the range (00000); to (77777)3 = 32768. You would need at least 6 wheels of size 8 for this job because that tally counter would go from (000000); to (777777); and (777777)3 = 262143. Your supervisor buys the tally counters from the Tally Counter Store (TCS). TCS sells customizable tally counters. You can purchase a tally counter with as many wheels as you wish. Each wheel can have as many digits as you wish. The price of a tally counter is the mimber of wheels multiplied by the size of each wheel. So the tally counter in the example above has 5 wheels each of size 10. This amounts to $50. A tally counter with 6 wheels each of size 8 would cost $48. So you could save 2 dollars.) You would like to find the cheapest tally counter. Exercise 1: For each value in the set {2,3,4,5,6,7,8,9}, compute the price of the cheapest tally counter with that particular wheel size. Exercise 2: (for fair effort completeness:) Is there a particular wheel size that will always give the optimal price? How does this relate to computer design? Is base 2 really the "best" base to be using? why or why not