Use Gauss-Jordan Elimination to solve: Use Gauss-Jordan Elimination to solve: Fi

ID: 3149080 • Letter: U

Question

Use Gauss-Jordan Elimination to solve: Use Gauss-Jordan Elimination to solve: Finite Mathematics Chapter 4 15. A dog food manufacturer makes two types of dog food: Sparky's Special Selection and Fido's Favorite Food. Each type of food uses two types of additives: Additive #1 and ve# of Additive #2. Each bag ofFido Favorite Food has 2 units of Additives and4 units of Additivew. On one day last month the OgToo manufacturerhad 151 units of Additive #1 anaT55units of Additive #2 available. How many bags of each typ ord gTo could e made to use exactly the amount of additives available? # Addictive i # Addictive X1 X 30b

Explanation / Answer

Let x = number of bags of SS to be made and y = number of bags of FF to be made. Then, the given conditions translate into the following equations:

5x + 2y = 151

3x + 4y = 155.

Or, put in matrix notation, Ax = y where

A = [5 2], x = [x], y = [151]

[3 4] [y] [155]

So, x = A-1y.

Solving the above matrix equation by Gauss-Jordan elimination method,

Elementary row operation

151

(1)

155

(2)

2/5

151/5

(3) = (1)/5

14/5

322/5

(4) = (2) – 3(3)

105/5 = 21

(5) = (3) - (6)(2/5)

322/14 = 23

(6) = (4)/(14/5)

Thus, 21 bags of SS and 23 bags of FF must be made ANSWER