Pancheros sells a variety of Mexican-inspired cuisine for which tortillas are often a main ingredient. Assume that each customer places an order requiring one tortilla with a 75% probability independent of other customers’ orders. The other 25% of customers place orders that do not require a tortilla. Assume that the number of customers who arrive per hour has a Poisson distribution with the average number of customers in an hour time slot given in the following table:

Pancheros currently prepares dough for 750 tortillas at the beginning of each day.
Due to uncertain customer demand, Pancheros may run out of tortillas, which affects profit as well as customer relations. Every tortilla-based customer order generates $2.35 in profit. Every customer who places an order requiring a tortilla but is denied (due to a tortilla stock-out) leaves Pancheros without buying anything with probability 0.13, and purchases a non-tortilla menu item (generating profit of $1.50) with probability 0.87.

a. Create a simulation model to generate the distribution of daily lost profit due to tortilla stock-outs.

b. What is the average daily lost profit? What is the 95% confidence interval on this mean?

c. On average, which hour of the work day does Pancheros run out of tortillas? What is the 95% confidence interval on the mean?

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Time of Day 11am-12pm 12pm-1pm 1pm-2pm Average Number of Customers 200 200 200 2pm-3pm 50 3pm-4pm 50 4pm-5pm 50 5pm-6pm 150 6pm-7pm 150 7pm-8pm 150 8pm-9pm 50 9pm-10pm 50