A dietitian wishes to plan a meal around three foods. the percentage of the daily requirements of proteins, carbohydrates, and iron contained in each ounce of the three foods is summarized in the following table food-i food-ii food-iii proteins (%) 10 6 8 carbohydrates (%) 10 12 6 iron(%) 5 4 12 determine how many ounces of each food the dietitian should include in the meal to meet exactly the daily requirement of proteins, carbohydrates, and iron (100% of each) by applying gauss seidal’s method.
Answers
Answer:
Food 1 = 2 Ounce
Food 2 = 6 Ounce
Food 3 = 4 Ounce
Step-by-step explanation:
Protein Carbohydrate Iron
Food 1 Contain - 10 6 8 2
Food 2 Contain - 10 12 6 6
Food 3 Contain - 5 4 12 4
To Have 100 % Protein
Food 3 Should be 2 , 4 , 6 , 8 ounces
Case 1 Food 2 is 2 Ounce
Then Food 1 + Food 2 = 9 ounces to have 100 % protein
& 8 * F1 + 6 * F2 = 100 - 24
=> 8 * F1 + 6*(9-F1) = 76
=> 2F1 = 22
=> F1 = 11 not possible
Case 1 Food 2 is 4 Ounce
Then Food 1 + Food 2 = 8 ounces to have 100 % protein
& 8 * F1 + 6 * F2 = 100 - 48
=> 8 * F1 + 6*(8-F1) = 52
=> 2F1 = 4
=> F1 = 2 & F2 = 7
Food 1 = 2 Ounce
Food 2 = 6 Ounce
Food 3 = 4 Ounce
Protein = 10* 2 + 10*6 + 5*4 = 100
Carbohydrate = 6*2 + 12*6 + 4*4 = 100
Iron = 8*2 + 6*6 + 12*4 = 100