Problem 2 You are the owner of a car racing team competing in the Formula 1…

Problem 2 You are the owner of a car racing team competing in the Formula 1 championship. The cars of your team require two different types of tires: (1) wet tires, which are suitable for driving under heavy rain conditions and (2) dry tires, which work better in sunny days. The number of tires needed by your team for each of the seven races of the championship are listed in Table 3 Type/Race 234567 Wet tires 30 20 40 55 80 150 180 Dry tires 35 2830|50 90150|200 Table 3: Demand of tires per race To satisfy the demand of tires required for each race you have two choices. One possibility is buying race and save the excess for subsequent races. You can also buy fewer tires that the ones you need, as long as you have enough tires in your inventory to fulfill the requirements. For instance, before race 1 you can buy 90 wet tires, which can be used in races 1, 2 and 3. Then, buy 65 tires before race 4, use 55 of those and save the residual 10 for race 5. Subsequently, buy the remaining 70 before that race, and finally buy 150 and 180 before races 6 and 7, respectively. The second option is recycling used tires. After each race, it is possible to recycle all, some, or none of the used tires that you currently have. The tires that are recycled are shipped to a recycling facility that adds rubber and reshapes them until they are as good as new. The recycling process is not immediate, though. If you decide to recycle used tires after a race, it will take the recycling company two races to send those back. For example, if you send 20 of the 30 tires used in race 1, those can only be used from race 3 and onwards. Notice that the combination of buying and recycling tires gives you many interesting options. For example, you can buy 30 wet tires the for the first race and send those to recycle after the race. Then, buy 30 tires before race 2, use 20 and save the remaining 10, which along with the recycled tires from race 1 will cover the demand of race 3. Suppose that the initial inventory of tires is zero.

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