A special diet needs to include exactly 340 units of calcium, 180 units of iron, and 220 units of vitamin A. the number of units per ounce of each ingredient for each of the foods is indicated in the table. units per ounce food A food B food C calcium 30 10 20 iron 10 10 20 vitamin A 10 30 20 A) how many ounces of each food must be used to meet the diet requirements? set up a 3x3 system of linear equations and solve it by Gauss-Jordan Elimination. B) how is the diet in part (A) affected if the vitamin A requirement is dropped?
A special diet needs to include exactly 340 units of calcium, 180 units of iron, and 220 units of vitamin A. the number of units per ounce of each ingredient for each of the foods is indicated in the table.
units per ounce
| food A | food B | food C | |
| calcium | 30 | 10 | 20 |
| iron | 10 | 10 | 20 |
| vitamin A | 10 | 30 | 20 |
A) how many ounces of each food must be used to meet the diet requirements? set up a 3x3 system of linear equations and solve it by Gauss-Jordan Elimination.
B) how is the diet in part (A) affected if the vitamin A requirement is dropped?
(a) Obtain the amount (in ounce) of each type of food used for the diet as follows.
Let x1 represents the number of ounces of food A, x2 represents the number of ounces of food B, and x3 represents the number of ounces of food C.
Given that, the diet includes exactly 340 units of calcium, 180 units of iron and 220 units of vitamin A.
The mathematical model for the problem with the given data and from the table can be formulated as follows.
This forms a system of linear equations.
Solve this system of linear equations by Gauss-Jordan elimination method as follows.
The augmented matrix is,
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