# During regular operations, an average gas station in Puerto Rico receives 30 customers every hour and can serve 45 customers each hour.

1.    During regular operations, an average gas station in Puerto Rico receives 30 customers every hour and can serve 45 customers each hour. After the hurricane, an average gas station received 72 customers every hours and service was reduced to 28 customers each hour due to reduced gas reserves. Assuming exponential distribution, simulate the gas station service for both conditions and compare values for average number in queue and waiting times.

2.    Customers at a fast food chain arrive at the drive thru window at an average rate of 1 every five minutes. The store uses one drive thru window for taking orders and paying. The average time to order, pay and receive the food is 6 minutes. They are considering separating the process and creating two windows; one for ordering and one for paying and receiving the food. They estimate the ordering window can process 1 customer every 2.5 minutes and the paying/receiving food can process 1 customer every 1.5 minutes. Compare the average number in queue and wait times for both scenarios and make a recommendation to the store. (remember that the scenario with 2 windows has a wait time for each window)

3.    A Kickstarter shoe manufacturer hired you as a consultant. She is trying to determine the amount of shoes to produce for a new Kickstarter campaign. Her material costs are \$43.50 per shoe and the manufacturing costs are \$27.50. Demand for her previous 3 campaigns was 1340, 1575 and 632 with an average profit of 25%. Unsold shoes are donated to a shelter and represent a loss of the materials and manufacturing costs.  She is considering producing 500, 1500, 2000 or 2500 shoes.

a.    Develop a model, run 1,000 trials and make a recommendation to the shoe manufacturer about the amount of shoes that she should produce to maximize her profits.

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