The Kellogg’s cereal production process used one cereal line to process two brands of cereal: wheat based Raisin Bran and corn-based Frosted Flakes. The line processed cereal in two stages: flake prepping and cooking-packaging. Stage 1: Flake Prepping The flake prepping stage began when raw corn grains or wheat flakes, depending on the cereal, entered a large, rotating pressure cooker, which used a screw to grind the raw materials into a flaky mash. Next, the mash entered a drying oven to remove excess moisture. Large, metal rollers then crushed the mash into thin flakes, which were ready for the cooking-packaging stage. The steps for stage one can be seen in Figure 1.Stage 2: Cooking-Packaging In the cooking-packaging phase, the prepped flakes entered a cereal cooker, at a rate of four tons of cereal per hour, where they were baked until turning golden-brown. Next, the baked flakes entered a coating drum that sprayed sugar and vitamins onto the flakes; the coating drum could process four tons of cereal per hour.8 Depending on which brand of cereal was being run, the cereal flakes entered one of two large hoppers that, in turn, fed a packaging line dedicated to that brand of cereal (see Figure 2). Thus, each brand of cereal had a dedicated hopper and packaging line. The packaging line was the last stage in the cereal production line and could package cereal at a rate of 1.5 tons per hour. Set-Up Time Between Runs The same cereal cooker and coating drum were used for both brands of cereal, but these two machines could process only one brand of cereal during a given run. After processing one brand of cereal for eight hours, the cereal cooker and coating drum were shut down, rigorously cleaned, and set up to produce the second brand of cereal. This precaution took four hours and ensured that there was no cross-contamination of cereal, which could be dangerous, even fatal, for consumers with allergies. Afterward, the production process resumed, running for eight hours with the second brand of cereal. While the cereal cooker and coating drum were shut down for cleaning, and while Frosted Flakes cereal was being run, Raisin Bran’s packaging line would continue operating as long as there was cereal in its hopper. Similarly, the packaging line for Frosted Flakes would continue operating while Raisin Bran was being run or while the cooker and coating drum were off. However, if a hopper was empty, its packaging line would shut down. The consultant realized that if Bryant extended the production time for both cereals, he could fill the hoppers with enough cereal so that the packaging lines would not starve at any point. To do this, the consultant would need to determine the optimal number of hours to run the cereal cooker and coating drum in order to produce the optimal amount of cereal in a run. If he could determine this value, Bryant knew that the plant’s production yield would increase, saving the Kellogg Company thousands of dollars of lost revenue every day. However, the consultant warned Bryant that extending the production time would cause the hoppers to carry more inventory. Surely, Bryant’s board would not be happy to see inventory levels rise. Bryant knew he needed the consultant’s help to address this issue. 1. If production time for either type of cereal is indeed eight hours, will the packaging lines work continuously at the rate of 1.5 tons/hour or will they be starved? Explain.2. In order for the packaging lines to work at the constant pace of 1.5 tons/hour without ever being starved, what should the production time for each product be? How many tons of cereal should each hopper be able to store?3. The consultant soon informs Bryant that cutting the setup time can lead to smaller production times for each product. If the Kellogg Company really aims on having eight-hour production runs for each product without ever starving the packaging lines of cereal, to what duration does the setup time need to be improved?