Cavity Candies mass produces an assortment of hard candies, consisting of three flavors: cinnamon, root beer, and grape. Bag 1 must have between 75 and 100 pieces of candy, with at least 40% being cinnamon, at least 30% being grape, and between 15% and 30% being root beer. Bag 2 must have between 50 and 75 candies, with no more than 30% cinnamon, at least 40% grape, and at least 20% root beer. Each bag can contain at most 60 cinnamon, 75 grape, and 75 root beer candies at costs of $0.01, $0.02, and $0.015 per candy, respectively. If bag 1 generates $0.03 per piece of candy in revenue, and bag 2 generates $0.025 per piece in revenue, formulate and solve a linear program to help maximize Cavity's per-bag profits?

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