Math Problem

[vamosj]

So working on this problem and I know of a solution without having to show my work, my problem is my understanding of the question itself in if I need to provide a mixture that has all three foods or if it has to to include any mix of them. The Guass Jordan Elimination Method has Row 3 zeroing out. Anyone help enlighten me if I'm going to right diretion.


A particular diet calls for
exactly 1000 units of vitamin A
exactly 1600 units of vitamin C
exactly 2400 units of vitamin E

An individual is fed a mixture of three foods.

Each gram of food 1 contains 2 units of vitamin A, 3 units of vitamin C, and 5 units of vitamin E.
Each gram of food 2 contains 4 units of vitamin A, 7 units of vitamin C, and 9 units of vitamin E.
Each gram of food 3 contains 6 units of vitamin A, 10 units of vitamin C, and 14 units of vitamin E.

How many grams of each food should the individual be fed to satisfy the diet requirements?

Identify your variables

Determine the system of equations

Use the Gauss-Jordan elimination method and solve the system of equations.

Report your solutions related to how much of each food should be fed to the individual.

[Gelston]

42

[DaCapn]

Your result, that one of the foods is not needed, is expected. Food 3 is just a linear superposition of foods 1 and 2. You can not form 3 linearly independent expressions.

[vamosj]

So how would I express that on row 3 of the Guass Jordan Method? My row three ended up as [0 0 0 | -200 ]

Should I just zero everything out or leave it as is?

[Cereal Killer]

Variables: x1, x2, x3 for food 1, 2, 3.

1000 = 2*x1 + 4*x2 + 6*x3
1600 = 3*x1 + 7*x2 + 10*x3
2400 = 5*x1 + 9*x2 + 14*x3

My solution is 1 = 300, 2 = 100. If it doesn't have any restrictions stated in the problem, like you can't use more than 200 grams of 1, then I wouldn't worry about not using 3.

I'm not sure what math you're in, but that would determine how you would be solving these equations. I can't remember off of the top of my head what a Gauss-Jordan Elimination is.

[Cereal Killer]

Oh shit, you're in linear algebra? [ 0 0 0 | -200 ] Is a no solution. You should be getting something more like [ 0 0 1 | 0 ] for your third line.

[vamosj]

Here's an example of the Guass Jordan Elimination Method. Yeah I'm not getting anything for my third line which is why this is dumbfounding me.


http://imgur.com/cu4yrpv

[Cereal Killer]

[2 4 6 | 1000]
[3 7 10 | 1600]
[5 9 14 | 2400]

Should be the start. My notation from here is the number of each line is enclosed in brackets [number]

1. Divide first row [1] by 2. (i.e. [1]/2 )
2. [2]-3*[1], [3]-5*[1]
3. [1]-2*[2], [3]+[2]
4. [3]/2
5. [1]-[3], [2]-[3]

Should yield x1=300, x2=100, x3=0