1. It will take 26 minutes to fill one rush order (6+2+10+5+2+1= 26 minutes). Gantt chart is also attached.
2. The cycle time is 10 minutes because the bottleneck is the time they have to wait for the cookies to bake in the oven. They cannot continue the cookie process without baking and the lack of room in the oven or additional ovens are the constraints that are limiting the total operation. The capacity of the operation would be 6 orders per hour (60 minutes/ 10 minutes= six orders), so that means you could fill 24 orders in one night (6 orders an hour * 4 hours). This answer does assume that every order only asks for one dozen each, for example, if one customer orders two dozen, you would only be able to fill 23 orders because that order would require using the oven twice.
3. The amount of labor per dozen for 1 order is 8 minutes per dozen (mixing and scooping takes 8 minutes) for Kristen and 4 minutes for Kristen’s roommate per dozen (the real work she does, the time she spends waiting is negligible so the 1 minute to load, 2 minutes to package and 1 minute to accept the payment). Kristen’s roommate only does slightly less work per dozen when they are all similar because she’ll only accept the payment once, so for two dozen she would do 3.5 minutes, and three dozen she would do 3.33 minutes per dozen. Kristen does the same amount of work per dozen when they are all different. When the cookies have similar ingredients, Kristen does less work because she doesn’t have to continue mixing for each dozen. If it’s two similar dozens of cookies, Kristen does 5 minutes of work per dozen (6 minutes of mixing, 2 minutes of scooping * 2 times/2). When it’s three similar dozens of cookies, Kristen does 4 minutes of work per dozen (6 minutes of mixing, 2 minutes of scooping * 3 times/3). If it’s two similar dozen and one different, she will do 6 minutes of work per dozen (6 minutes of mixing* 2 times, 2 minutes of scooping * 3 times/3). Kristen still does 3.5 and 3.33 minutes of work per dozen because her process doesn’t change based on the variety of cookies.
4. I personally wouldn’t because the operation is slow enough and it would incentivize customers to buy more which isn’t necessarily a good thing for the reputation of Kristen’s cookies in terms of its speed of service. People will probably order different dozens of cookies and as we saw, it didn’t speed up Kristen’s operations which in terms of labor is the most timely. I think this would get more money in the short run, but in the long run people wouldn’t be too happy with Kristen’s speed if everyone ordered three dozens of cookies at a time (some orders wouldn’t be received within hours.)
5. Without any more oven space, buying more electric mixers would not be too beneficial because the bottleneck is the oven. At the moment, Kristen is actually continually waiting on oven space to be available which is what is slowing operations down, so I would stay with one since it would just increase your fixed costs. As for the trays, I would have four, because you could have one tray in the oven and still be able to scoop out the contents of the processor for three dozen cookies which would maximize Kristen’s efficiency and she wouldn’t be waiting.
6. The oven is the bottle neck because it takes the most time and the operations cannot continue without baked cookies. Kristen cannot make more cookies without space in the oven, and her roommate cannot continue to finish the order without the baked cookies either. Adding another oven (assuming it only took one dozen still), would increase the capacity to 10 orders an hour because the bottle neck would become washing and mixing the ingredients which would be 1 minute more per dozen in the process. The new constraint for baking would be 5 minutes because there are two ovens now that it decreases the respective cycle time for baking by half. The maximum amount I would pay for an additional oven would be the increased revenue it generates per month for Kristen’s cookies, because past that the oven wouldn’t be seeing a return on the investment.