Calories protein( in grams) Vitamin C (in milligrams) Food A 40 10 20 Food B 500...
| Calories | protein( in grams) | Vitamin C (in milligrams) | |
|
Food A |
40 | 10 | 20 |
| Food B | 500 | 5 | 50 |
| Food C | 200 | 2 | 300 |
Three foods have the nutritional content per ounce shown in the table to the right. If a meal consisting of the three foods allows exactly 740 ?calories, 17 grams of? protein, and 930 milligrams of vitamin? C, how many ounces of each kind of food should be? used?
Homework Answers
Let x, y, z ounces of Food A,B,C respectively be used. Then 40x+500y+200z = 740…(1), 10x+5y+2z = 17…(2) and 20x+50y+300z = 930…(3).
The augmented matrix of this linear system is A (say) =
|
40 |
500 |
200 |
740 |
|
10 |
5 |
2 |
17 |
|
20 |
50 |
300 |
930 |
To solve the above linear system, we will reduce A to its RREF as under:
Multiply the 1st row by 1/40
Add -10 times the 1st row to the 2nd row
Add -20 times the 1st row to the 3rd row
Multiply the 2nd row by -1/120
Add 200 times the 2nd row to the 3rd row
Multiply the 3rd row by 1/280
Add -2/5 times the 3rd row to the 2nd row
Add -5 times the 3rd row to the 1st row
Add -25/2 times the 2nd row to the 1st row
Then the RREF of A is
|
1 |
0 |
0 |
1 |
|
0 |
1 |
0 |
1/5 |
|
0 |
0 |
1 |
3 |
It implies that x = 1, y = 1/5 and z = 3. Thus, 1, 1/5 and 3 ounces of Food A,B,C respectively should be used.
Add Answer to:
Calories
protein( in grams)
Vitamin C (in milligrams)
Food A
40
10
20
Food B
500...
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