Unsure if this work is on the right track

RC= Batch Size / (Setup time + Batch Size * Activity Time)

Problem 1 Calculate the resource capacities of each step in the doughnut-making process. What is the bottleneck of the process? What is the capacity of the process? Problem 2 How would your answers in Problem 1 change if the batch size was doubled to 16lbs? You may assume that the activity times and the setup times for each step do not change when you change batch size. Problem 3 If Johnson decides to keep the batch size at 8lbs and instead focus on reducing the setup time for the extrusion process, by how much must he reduce the setup time in order to meet his demand? Problem 4 If Johnson decides to invest in the set of 6 cutters, what setup time would be needed for Johnson to meet demand with 6 cutters using the standard 8lb batch? Problem 5 What do you think Johnson should do?

Dewey Johnson sat in his office contemplating the past year of operation of his Dooly County Doughnuts (DCD) shop located in Vienna, Georgia. DCD served walk-in customers, and also made doughnuts to be stocked at local grocery stores and coffee shops. Over the past year, Johnson had spent considerable time trying to increase sales but had not spent much time focused on the operations of the shop. Through his window, he could see the line for doughnuts extending well into the parking lot. While he was pleased with the results of his sales push, he realized he needed to assess his capacity and maybe consider expansion. Product Sales Doughnut production at DCD was currently limited to a single 8-hr. shift per day, 7 days per week. During peak hours, Johnson maintained a staff of 3 to 4 employees that was more than capable of running the highly automated process without any additional slowdowns. Currently Johnson sold, on average, 1,100 dozen doughnuts per day of all varieties. Production The doughnut-making process consisted of four stages: (1) batching, (2) mixing, (3) production, and (4) customizing. See Exhibit 1 for a layout of the process. Stage 1: Batching The batching stage started with an operator combining all the ingredients in a mixing bowl. Water was added first, followed by all of the dry ingredients contained in DCD's proprietary doughnut recipe. It took 2min. to place the ingredients in the mixing bowl.. The equipment could handle batches of dough of various sizes ranging from just 2lb. to over 20lb. Each doughnut required exactly 2oz. of dough. Stage 2: Mixing Once all of the ingredients had been combined, the batch was placed in the mixer. The mixing process took 2.5min. per batch, and the mixer tumed off automatically at the end of the process. The store had 2 mixers. In the customizing stage, doughnuts were customized to either be placed for sale at the counter or boxed for specific customer orders. This step involved adding a range of different toppings - from traditional toppings like sprinkles to unique toppings such as the Ellis Brothers' world-famous pecans from right up the road. One employee handled the customization step. On average, the employee was able to customize two doughnuts every 3.5sec. The Problem Johnson had noticed a disturbing trend. Each day, DCD was turning away customers because it was unable to make enough doughnuts to meet demand. He needed to find a way to increase his capacity. One change Johnson had considered was to increase the batch size. The standard batch size that he had instructed his employees to use was 8lb. The mixer and the extruder could handle much larger batches, however, he wanted to keep the batches as small as possible so as to not wear out his equipment prematurely. Alternatively, the staff had suggested there might be a way to keep the current batch size, and instead, focus on improving some of the more manual steps in the current process to increase capacity. Finally, Johnson knew that the extruder could be modified to operate with 6 cutters and increase the rate at which doughnuts could be extruded. He was cautious regarding this option though since setting up the extruder for 6 cutters would take longer than the setup time required for the existing 3 cutters. Stage 3: Production The production stage consisted of three steps: (1) extruding, (2) frying, and (3) glazing. Extruding After mixing, the dough was transferred into the extrusion machine container. There the dough was pushed through cylindrical cutting attachments (cutters) that extruded the dough into individual pieces that would eventually be turned into the finished doughnut: The machine used a set of 3 cutters. Each cutter could extrude dough at a rate of 18 extrusions per minute. Therefore, using 3 cutters, the machine made doughnuts at a rate of 54 doughnuts per minute. The machine had to be set up before each batch was extruded. This included cleaning the machine from the previous batch, cleaning the cutters, and adding the fresh batch of dough. The setup took approximately 1,5min. per batch. Frying After being formed by the extruder, the doughnuts were dropped directly into hot shortening in a long and narrow fryer. The fryer ran continuously and had sufficient space to handle as many doughnuts as the extrusion machine provided. The doughnuts stayed in the fryer for 90sec. Surface rods pushed the doughinuts through the fryer. Glazing The fried doughnuts cooled on a conveyor for 45sec. before passing through the glazing machine. The cooling conveyor and glazer also ran continuously and had sufficient space to handle as many doughnuts as the extrusion machine provided, so finished doughnuts were produced at the rate at which they were made by the extrusion machine. Stage 4: Customizing In the customizing stage, doughnuts were customized to either be placed for sale at the counter or boxed for specific customer orders. This step involved adding a range of different toppings- from traditional toppings like sprinkles to unique toppings such as the Ellis Brothers' world-famous pecans from right up the road. One employee handled the customization step. On average, the employee was able to customize two doughnuts every 3.5sec