Using Arena, complete the simulation of the following problems (show all your work). For each of the problems obtain the report from Arena, and interpret the following:

o Cycle time: This is the average time it takes for an entity to traverse the entire system, from entry to exit. o Resource utilization: This is essential to ensure that resources (e.g., machines, workers) are used efficiently. o Queue lengths: Keeping track of queue lengths at different points in the system is crucial to identify congestion and potential delays.

1. A company manufactures 3 products, which are "put together" to form a single product. This final product requires 3 units of product 1, 2 units of product 2, and 1 unit of product 3. The input for the type 1 product has a time between arrival UNIF (2.4) minutes and its production time is TRIA (3,3.5,4.2) minutes. The input for the type 2 product has a time between arrivals EXPO (3.5) minutes and its production time is UNIF (3.5,4.4) minutes. The input for the type 3 product has a time between arrival NORM (6,0.5) minutes and its process time for its production is NORM (4,0.2) minutes. After each product is produced, it must be assembled according to the requirements of the final product. Assembly time is TRIA (1,1,5,2) minutes.

You want to simulate 6 hours of production with 20 replicas. It is known that in the current process, there is a different operator for each type of production process, for each product, and also a special operator for assembly. The performance measures you want to analyze are the average cycle time and the manufactured finished products.

a. What would happen if one more operator was added for the production process of product 1 and product 2?

b. What would happen if one more operator was added to the production process of product 1? c. What would happen if one more operator was added to the production process of product 2? d. What would happen if you didn't increase resources, but instead reduced the production time of products 1 and 2 by 30% with a process improvement? e. What if the company now wants the finished product to contain 3 units of product 1, 3 units of product 2, and 1 unit of product 3 and maintain the current resources and current times?

2. A soft drink bottling plant has 2 production lines: the family size line and the personal or individual size line. The containers arrive with an exponential distribution by an average of 15 seconds. 65% are individual-sized packaging. The filling time varies uniformly between 8 and 12 seconds for the individual size and between 14 and 20 seconds for the large size. An automated check station lasting 3 seconds rejects 15% of the bottles. The approved bottles go to the packaging where boxes of 4 individual-size bottles and 6 packs of family bottles are formed. Visualize the number of defective bottles and the number of finished boxes. For family and individual size, record the number of defective bottles and the number of finished boxes. Simulate 5 hours.

a. What would happen if the arrival rate of the containers is reduced to 10 seconds? b. What would happen if the filling times were changed to uniform distributions between 10 to 14 seconds for the individual size and 16 to 22 seconds for the family size? c. What would happen if the rejection rate of the checking station is increased to 20%? d. What would happen if the percentage of individual-sized packages is increased to 75%?

SOLVE BOTH EXERCISES