Your company assembles two components into a finished product. You get component 1 from one supplier and component 2 from another supplier. You just received an order for the product, so you immediately request a component 1 and a component 2 from the suppliers. The shipping times for the suppliers are independent random variables, each triangularly distributed with minimum 24 hours, most likely value 30 hours, and maximum 60 hours. (Assume for simplicity that your company operates 24 hours a day and can receive a shipment at any time of day.) You can start assembly any time after both components are received.

The assembly time takes a triangularly distributed amount of time to complete, with minimum, most likely, and maximum times of 12 hours, 15 hours, and 30 hours, respectively. Finally, you ship the product to the customer, and this shipping time is triangularly distributed with parameters 24, 36, and 60 hours.

a. If the random times were not random but were instead replaced by their means, how many hours would it take for the customer to receive the product?

(Note: The mean of a triangular distribution is the average of its three parameters.)

b. Using simulation, what can you say about the distribution of time (hours) it takes for the customer to receive the product? How does the mean of this distribution compare to your answer from part a?