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Weekday lunch demand for spicy black bean burritos at the Kiosk, a local snack bar, is approximately Poisson with a mean of 22. The Kiosk charges $4.00 for each burrito, which are all made before the lunch crowd arrives. Virtually all burrito customers also buy a soda that is sold for 600. The burritos cost the Kiosk $2.00, while sodas cost the Kiosk 50. Kiosk management is very sensitive about the quality of food they serve. Thus, they maintain a strict "No Old Burrito" policy, so any burrito left at the end of the day is disposed of. The distribution function of a Poisson with mean 22 is as follows:
Q
F(Q)
1
0.0000
2
3
4
5
6
0.0001
7
0.0002
8
0.0006
9
0.0015
10
0.0035
11
0.0076
12
0.0151
13
0.0278
14
0.0477
15
0.0769
16
0.1170
17
0.1690
18
0.2325
19
0.3060
20
0.3869
21
0.4716
22
0.5564
23
0.6374
24
0.7117
25
0.7771
26
0.8324
27
0.8775
28
0.9129
29
0.9398
30
0.9595
31
0.9735
32
0.9831
33
0.9895
34
0.9936
35
0.9962
36
0.9978
37
0.9988
38
0.9993
39
0.9996
40
0.9998
a. Suppose burrito customers buy their snack somewhere else if the Kiosk is out of stock. How many burritos should the Kiosk make for the lunch crowd?
b. Suppose that any customer unable to purchase a burrito settles for a lunch of Pop-Tarts and a soda. Pop-Tarts sell for 75¢ and cost the Kiosk 25¢. (As Pop-Tarts and soda are easily stored, the Kiosk never runs out of these essentials.) Assuming that the Kiosk management is interested in maximizing profits, how many burritos should they prepare?
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