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
|
0.0000
|
|
3
|
0.0000
|
|
4
|
0.0000
|
|
5
|
0.0000
|
|
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?