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?

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