A young boy is a budding entrepreneur and decides to start his career by selling sandwiches in an office building. He buys each sandwich for $3.50 and he then sells each sandwich for $5.75, making a nice profit of $2.75 per sandwich sold. However, he is out the $3.50 for each sandwich that he doesn't sell.
The boy has tracked demand over his first few months and he has determined that the following probability distribution correctly captures the demand for sandwiches each day:
| x |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| p(x) |
0.02 |
0.03 |
0.05 |
0.10 |
0.15 |
0.20 |
0.20 |
0.15 |
0.07 |
0.03
|
- What will a typical day look like in terms of sandwich demand?
- How many sandwiches should he bring each day in order to maximize his expected profits?