A dietitian is planning a meal of beef rice and carrots for

A dietitian is planning a meal of beef, rice, and carrots for a patient. The patient needs the meal to contain 81.8 grams of carbohydrate, 20.2 grams of protein and 7.2 grams of fat. The table below shows the number of grams of carbohydrate, protein, and fat in 100 grams of each food. (Note, the total is not 100 grams due to the water and fiber content of the food.) How much of each food should be used so that the patient gets the needed nutrients?

Solution

Here we are given

Carbohydrate Protein Fat
beef 1C 22P 12F
Rice 25C 2P 0F
carrots 8C 1P 0F

C >= 81.8
P >= 20.2
F >= 7.2
C = a + 25b + 8c
P = 22a + 2b + c
F = 12a + 0b+0c

we will apply Matrix to solve for a,b and c

Find the pivot in the 1st column in the 1st row

Multiply the 1st row by 22

Subtract the 1st row from the 2nd row and restore it

Multiply the 1st row by 12

Subtract the 1st row from the 3rd row and restore it

Make the pivot in the 2nd column by dividing the 2nd row by -548

Multiply the 2nd row by 25

Subtract the 2nd row from the 1st row and restore it

Multiply the 2nd row by -300

Subtract the 2nd row from the 3rd row and restore it

Make the pivot in the 3rd column by dividing the 3rd row by -0.19708029197079213

Multiply the 3rd row by 0.016423357664232974

Subtract the 3rd row from the 1st row and restore it

Multiply the 3rd row by 0.3193430656934307

Subtract the 3rd row from the 2nd row and restore it

Solution set:

a = 0.6000000000000176

b = 2.80000000000011

c = 1.399999999999654