Each group of commands and outputs included in the Word file MUST NOT be edited.

[A word problem involving Linear Algebra in MATLAB]

You wish to prepare a meal containing certain amounts of fat, carbohydrate and protein. Your ingredients are yogourt, flax, and bran. You carefully read the package labels and determine the following information:

Yogourt flax Bran
Per 125 Per 13g Per 15g
Fat : 1g 4.5g 0.5g
Carbohydrate:8g 4g 10g
Protein: 5g 3g 2g

For example 125g of yogourt contains 5g of protein.

You now wish to prepare a dish that will contain 5g of fat, 40g of carbohydrate and 15g of protein.

Your task is to find the amount of yogourt, flax, and bran that will have the appropriate total amounts of fat, carbohydrate and protein.

1. Re-state the table above in terms of the ratios of fat, carbohydrate and protein that are found respectively in yogourt, flax, and green lentils. For example, there is 5g of protein in 125g of yogourt, so the ratio is 0.04 (=5/125) Use one or more MATLAB calculations, and keep 4 significant digits.
2. Define your UNKNOWN variables, by hand. Explain any assumptions about units.
3. Set up the equation in terms of a system of simultaneous equations, written by hand, not in MATLAB
4. EXPLAIN how you obtain each equation, using a combination of words, variables and numbers.
5. Write the system of equations in MATLAB with comments.
6. Define your unknown vector in terms of the unknown variables in #2
7. Solve the system of equations using MATLAB.
8. Check your work using MATLAB. Note: parts 5-8 should consist of one contiguous unedited chunk of MATLAB comments, code and output
9. State the values of each variable found.
10. Interpret the output in terms of the problem domain, to state your overall answer.