Question

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

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. 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?

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Answer #1

Create spreadsheet model as follows:

T H 4 A Ⓡfx =SUMPRODUCT(B4:G4,$B$13:$G$13) B C D E F G Susans meals Toms meals Food A Food B Food C Food A Food B | Food C

EXCEL FORMULAS:

Susan's meals Tom's meals
Food A Food B Food C Food A Food B Food C
Total 1 1 1 1 1 1 =SUMPRODUCT(B4:G4,$B$13:$G$13)
Calcium 30 25 20 =SUMPRODUCT(B6:G6,$B$13:$G$13) >= 400
Iron 1 1 2 =SUMPRODUCT(B7:G7,$B$13:$G$13) >= 20
Vitamin C 2 5 4 =SUMPRODUCT(B8:G8,$B$13:$G$13) >= 50
Calcium 30 25 20 =SUMPRODUCT(B9:G9,$B$13:$G$13) >= 350
Iron 1 1 2 =SUMPRODUCT(B10:G10,$B$13:$G$13) >= 15
Vitamin C 2 5 4 =SUMPRODUCT(B11:G11,$B$13:$G$13) >= 40
Result:

Enter Solver Parameters as follows:

S Solver Parameters Set Objective: $H54 To: Max Min value of: 0 By Changing Variable Cells: $B$13:$G$13 Subject to the Constr

Click Solve to generate the solution:

H4 A B @ fx =SUMPRODUCT(B4:G4,$B$13:$G$13) C D E F G Susans meals Toms meals Food B Food Food A Food B Food C K L M N O P Q

Optimal solution:

Susan's meals: Food A = 7.50 oz, Food B = 3.33 oz, Food C = 4.58 oz

Tom's meals: Food A = 7.50 oz, Food B = 3.33 oz, Food C = 2.08 oz

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