Hello,

Below is the question: You operate a business specializing in heat-treating industrial castings. Each day, the number of castings you receive for treatment follows a Poisson distribution with a mean of 4.1. These castings are processed in a high-temperature oven that can hold up to 5 castings at a time. The oven uses a heating element with the following probabilities of failure depending on the day of use: Day 1: 1% Day 2: 7% Day 3: 9% Day 4: 15% Day 5: 25% After the fifth day of use, safety regulations require that the heating element be replaced, even if it is still functioning. If the heating element fails on any day, you must wait until the next day to reprocess all castings scheduled for that day. When the heating element is functioning, you can process up to 5 castings per day, but if it fails, your processing capacity drops to 0. You process castings on a first-come, first-served basis. If you cannot finish all castings on a given day, the unprocessed castings are saved in a queue to be processed the next day. You are considering five policies, parameterized by a number = 1 , 2 , 3 , 4 , d=1,2,3,4, or 5 5. If the heating element has been used for d days and has not failed, you replace it at the end of the day. If the element fails, you replace it immediately at the end of the day. The economic factors of the operation are as follows: Replacing the heating element costs $800 if it has not failed. Replacing the heating element costs $1500 if it has failed. You receive $200 in revenue for each casting processed. Each day a casting remains unprocessed in the queue costs you $40 in loss of goodwill, storage, etc. All other costs and revenues can be assumed negligible. Determine by simulation which value of d yields the highest expected profit over a 60-day period. You can ignore any costs and revenues from castings left in the queue at the end of the period. Assume you start with a new heating element on the first day. Additionally, assess whether the queue of unprocessed castings exceeds 10 at any time during the 60-day period with the optimal value of d. What is the probability of this occurrence? Run 5000 iterations in @risk excel.

Please solve this using @RISK addin in excel only.