Explanation Given Information: In the annual Song Festival, Duffin house will serve three kinds of granola: granola treats, nutty granola treats and nuttiest granola treats. The table shows the required ingredients to make a single serving of each type of granola and also the total amount of each ingredient. All the ingredients are to be used as decided by the annual song festival planners. Granola ( x ) Nutty Granola ( y ) Nuttiest Granola ( z ) Total Available Toasted oats 1 1 5 1,500 Almonds 4 8 8 10,000 Raisins 2 4 8 4,000 Formula Used: Elementary row operations: Type 1: Replacing the row R i by a R i , where a is a nonzero number. Type 2: Replacing the row R i by a R i ± b R j , where a is a nonzero number. Gauss Jordan reduction method: Step 1: First clear the fractions or decimals if any. Step 2: Pivot the first nonzero element of the first row. Step 3: Use the pivot to clear its column. Step 4: Pivot the first nonzero element in the second row and clear the column. Step 5: Pivot the first nonzero element in the third row and clear the column. Step 6: Turn all the pivot elements into a 1. Calculation: Firstly identify and label the unknowns. Considering the provided information the unknowns should be labelled like this, x = The number of servings of granola y = The number of servings of nutty granola z = The number of servings of nuttiest granola Consider the table provided, Granola ( x ) Nutty Granola ( y ) Nuttiest Granola ( z ) Total Available Toasted oats 1 1 5 1,500 Almonds 4 8 8 10,000 Raisins 2 4 8 4,000 Now, the required totals ingredients in the table provided will result in three linear equations: x + y + 5 z = 1500 4 x + 8 y + 8 z = 10000 2 x + 4 y + 8 z = 4000 The augmented matrix for the obtained system of equations is: [ 1 1 5 1500 4 8 8 10000 2 4 8 4000 ] Apply Gauss Jordan reduction method to get the solution of the given system of equation. Begin by simplifying the rows of the matrix by the operation R 2 → 1 4 R 2 , R 3 → 1 2 R 3 [ 1 1 5 1500 4 8 8 10000 2 4 8 4000 ] → [ 1 1 5 1500 1 2 2 2500 1 2 4 2000 ] Now, pivot the first nonzero element of first row and clear its column Perform the operation R 2 → R 2 − R 1 , R 3 → R 3 − R 1 , [ 1 1 5 1500 1 2 2 2500 1 2 4 2000 ] → [ 1 1 5 1500 0 1 − 3 1000 0 1 − 1 500 ] Now, pivot the first nonzero element of second row and clear its column

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 4, Problem 36RE

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To calculate: The amount of each type of granola they can make.

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Chapter 4, Problem 35RE

Chapter 4, Problem 37RE

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Chapter 4 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...

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The amount of each type of granola they can make.

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