Here is the nutritional information for 20 fl oz of Original Coke®, Vanilla Coke®, Pepsi Ⓡ and Pepsi Next Ⓡ, represented

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Here Is The Nutritional Information For 20 Fl Oz Of Original Coke Vanilla Coke Pepsi And Pepsi Next Represented 1 (172.48 KiB) Viewed 36 times

Here is the nutritional information for 20 fl oz of Original Coke®, Vanilla Coke®, Pepsi Ⓡ and Pepsi Next Ⓡ, represented as nutritional vectors with the respective amount of Calories, Sodium (mg) and Carbs (g): 100 100 70 25 The nutritional vector for original coke is noc can be expressed as a linear combination of vectors of the other colas: noc=anvc+Bnp+mpN noc = where the coefficients are 240 (26) 75 65 ₂nvc= 260 α = 1/2 B = 7/21 Note: this may be a tricky calculation, see hints below. Calories Sodium (mg) Carbs (g) ,np = Table 1. Ingredients and Nutritional Information Carbonated Water (1 fl oz) 0 5 0 The main ingredients of cola are Carbonated Water, High Fructose Corn Syrup (HFCS) and Caramel Colour. The nutritional content for these ingredients is in the table below We can represent this nutritional information by the matrix A: A = 250 (55). 70 50 " 0 25 25 1 20 5 38 HFCS (1 fl oz) 25 1 5 and npN= Y = 4/15 Caramel Colour (1 fl oz) 25 20 38

We can represent this nutritional information by the matrix A: A The matrix A defines a linear map from ingredient vectors to nutritional vectors. For example, we can compute the nutritional value of a mixture of 8 fl oz of Carbonated Water, 5 fl oz of HFCS and 1fl oz of Caramel Colour as: 8 (9) A = The ingredient vector for Pepsi is But with the power of linear algebra, we can also go backwards and compute the following valuable trade secrets (see hints below, and give your answers to two significant figures): . The ingredient vector for Vanilla Coke is 0 25 25 1 20 5 0 5 38 A-¹ nvc= А A-¹np = • The ingredient vector for Pepsi Next is A-¹nPN -1 - 7.8 9.9 .55 & P • the Maple command to compute the inverse N of the matrix M is & P. Hints • the Maple command for finding the reduced row-echelon form of a matrix M is LinearAlgebra [ReducedRowEchelonForm] (M); N = LinearAlgebra [MatrixInverse] (M) ; • the Maple command to compute the product of a matrix N and vector v, evaluated to two significant figures, is evalf [2] (LinearAlgebra [Multiply] (N, v) ) ;