This question is about the application of linear programming (LP). Part (b) is a continuation of Part (a), and Part (c) is not related to Parts (a) and (b). (a) Mary's breakfast is a mix of two cereals: C1 and C2. The nutritional content (per 100 g (grams)) and price (per kg (kilogram)) of the two cereals are shown in Table 1. E.g., every 100 g of cereal C1 contains 10 g of protein. According to nutrition experts, Mary should eat at least 40 g of cereal for breakfast, and thus get at least 6 g of protein and at least 2 g of fiber from it. Mary likes the taste of C2, so she wants C2 to be at least 50% of the mix. The question is how to mix the two cereals in each breakfast so that Mary gets the amount of nutrients she needs at the lowest cost?

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Table 1. The nutritional content and price of the two cereals Nutritional content per 100 g of cereal Cereal C1 Protein (g) 10 C2 10 Fibre (g) 13 5 Cost ($/kg) 12 16 Table 1. The nutritional content and price of the two cereals Nutritional content per 100 g of cereal Cereal C1 Protein (g) 10 C2 10 Fibre (g) 13 5 Cost ($/kg) 12 16