precalculus matrix

Question

Bob, a nutritionist who works for the University Medical Center, has been asked to prepare special diets for two patients, Susan and Tom. Bob has decided that Susan's meals should contain at least 400 mg of calcium, 20 mg of iron, and 50 mg of vitamin C, whereas Tom's meals should contain at least 350 mg of calcium, 15 mg of iron, and 40 mg of vitamin C. Bob has also decided that the meals are to be prepared from three basic foods: Food A, Food B, and Food C. The special nutritional contents of these foods are summarized in the accompanying table. Find how many ounces of each type of food should be used in a meal so that the minimum requirements of calcium, iron, and vitamin C are met for each patient's meals.

Answer 1

Here is the table that you did not provide

Food A Food B Food C

Amt Calcium A Aa Ba Ca

Amt. Iron. Ab Bb Cb

Amt. Vit C Ac Bc Cc

Sa, Sb, and Sc are the amount of each food for Susan.

Ta, Tb, and Tc are the amount of each food for Tom.

Sa*Aa + Sb*Ab + Sc*Ac = 400

Sa*Ba + Sb*Bb + Sc*Bc = 20

Sa*Ca + Sb*Cb + Sc*Cc = 50

Ta*Aa + Tb*Ab + Tc*Ac = 350

Ta*Ba + Tb*Bb + Tc*Bc = 15

Ta*Ca + Tb*Cb + Tc*Cc = 40