The Stage 1 Case

The Happy Toy Company’s R&D department is always looking for great ideas for new toys. On average, the R&D department generates about 10 new toy ideas a week. To go from idea to approved product, the idea must go through 5 stages: https://d2vlcm61l7u1fs.cloudfront.net/media%2F9cb%2F9cbcf687-036b-4fb6-b54e-a05363a1ddb4%2FphpLrJfO9.png In initial screening a staff member spends 2 hours considering the idea. In mock-up, the idea is sent to one of many suppliers to produce a physical mock-up of the toy. There is essentially unlimited capacity at this stage, but it takes 4 days to get the mockup built even though multiple mockups can be built simultaneously. In safety testing each idea requires 2 days from a staff member to have the idea checked for safety. In focus groups each idea requires 3 hours from a staff member to have the idea test marketed. Finally, the management team meets for 4 hours per idea to decide if the toy should be added to its line of products sold to customers. At the end of each stage, successful ideas enter the next stage. All other ideas are dropped. The following table summarizes the process: https://d2vlcm61l7u1fs.cloudfront.net/media%2F54e%2F54e0586d-79fb-4cbe-9e67-6cd428988122%2FphpQMorPW.png For example, there are 7 staff members that work in the safety stage. In each stage each idea is processed by only one staff member: for example, once one of the 7 staff members starts working on an idea in the safety stage, the idea completes that stage in 2 days (and either exits or moves to the focus group stage). Everyone works 8 hours per day, 5 days a week. a)On average, how many ideas are in the mock-up stage? b)Which stage has the highest implied utilization (as a %)?