Bob, a nutritionist who works for the University Medical Center, has been asked to prepare special...

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Bob, a nutritionist who works for the University Medical Center,has been asked to prepare special diets for two patients, Susan andTom. Bob has decided that Susan's meals should contain at least 490mg of calcium, 23 mg of iron, and 60 mg of vitamin C, whereas Tom'smeals should contain at least 440 mg of calcium, 18 mg of iron, and50 mg of vitamin C. Bob has also decided that the meals are to beprepared from three basic foods: Food A, Food B, and Food C. Thespecial nutritional contents of these foods are summarized in theaccompanying table. Find how many ounces of each type of foodshould be used in a meal so that the minimum requirements ofcalcium, iron, and vitamin C are met for each patient's meals.
Contents (mg/oz)
Calcium Iron Vitamin C
Food A 30 1 2
Food B 25 1 5
Food C 20 2 4
Susan's meals:
Food A     oz
Food B     oz
Food C     oz

Tom's meals:
Food A     oz
Food B     oz
Food C     oz

Answer & Explanation Solved by verified expert

3.7 Ratings (427 Votes)

Let Susans meal consist of x y and z oz of Food ABCrespectively and let Toms meal consist of a b and c oz of FoodABC respectivelyThen 30x25y 20z 490 or on dividing both the sides by 56x5y4z 981xy2z 23 2 and2x5y 4z 603Also 30a25b 20c 440 or on dividing both the sides by 56a5b4c 88 4 ab2c 18 5 and 2a5b 4c 506Now on multiplying both the sides of the See Answer

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