# (Solution) : Q12.10** ( The Kiosk ) Weekday lunch demand for spicy black

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Q12.10** ( The Kiosk ) 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 60¢. The burritos cost the Kiosk \$2.00, while sodas cost the Kiosk 5¢. 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:

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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

Q F(Q)

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

Q F(Q)

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

Q F(Q)

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?

The problem is similiar to newspaper vendor problem.

As per the given data , profit per unit sale of burrito = \$2 (\$4 sales price – \$2 cost alongwi

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