A pediatric dietician at an innercity foundling hospital nee

A pediatric dietician at an inner-city foundling hospital needs to supplement each bottle of baby formula given to three infants in her ward with the units of vitamin A, vitamin D, calcium, and iron given in the first table. If four diet supplements are available with the nutrient content per drop given in the second table, how many drops of each supplement per bottle of formula should each infant receive?

Units per Drop

Supplement 1

Supplement 2

Supplement 3

Supplement 4

Vitamin A

5

0

4

4

Vitamin D

3

1

2

2

Calcium

0

3

3

2

Iron

1

6

7

5

Units Needed

Billy

Susie

Jimmy

Vitamin A

48

46

47

Vitamin D

26

26

26

Calcium

19

27

19

Iron

49

65

49

Units per Drop	Supplement 1	Supplement 2	Supplement 3	Supplement 4
Vitamin A	5	0	4	4
Vitamin D	3	1	2	2
Calcium	0	3	3	2
Iron	1	6	7	5

Solution

Let number of drops required for supplement one be S1,supplement two be S2 and similarly S3 and S4.

For Billy , 5S1+4S3+4S4=48 3S1+S2+2S3+2S4=26 3S2+3S3+2S4=19 S1+6S2+7S3+5S4=49

solving these we get S1=4, S2=1,S3=2,S4=5 So, Billy requires 4 drops of supplement 1, 1 drop of supplement 2, 2 drops of supplement 3 and 5 drops of supplement 4.

For Susie , 5S1+4S3+4S4=46 3S1+S2+2S3+2S4=26 3S2+3S3+2S4=27 S1+6S2+7S3+5S4=65

Similarly soving these we get,S1=4, S2=1,S3=3,S4=6

For Jimmy, 5S1+4S3+4S4=47 3S1+S2+2S3+2S4=26 3S2+3S3+2S4=19 S1+6S2+7S3+5S4=49  

Similarly soving these we get,S1=4, S2=1,S3=2,S4=5