PROMPT: Suppose you open a lemonade stand on the side of the street.

Potential buyers drive by according to a Poisson process (Nt)t0 with rate 1. The i-th

buyer is willing to pay up to Xi for lemonade, where Xi are i.i.d. uniform [0; 1] random

variables, but you are only allowed to display one price and if the buyer doesn't like it

they'll just drive past. Suppose it costs you c = 0:2 to produce one lemonade.

(a) Suppose you can run the lemonade stand all day, i.e. for the interval [0; 24]. What

price p should you charge to maximize profit?

(b) Suppose you only have enough lemon juice to sell 5 lemonades in a day. What price

p should you charge to maximize profit?

I solved part a by finding an expression for the total profit in terms of the sale price, p. I found the optimal sale price, p*, to be 0.4 by setting the derivative of my expression equal to 0. Assuming my part a is correct (or regardless), how do we solve part b?

Thank you. Very much appreciated!