Aperson is ordered by doctor to take 22 units of vitamin a, 18 units of vitamin d, and 11 units of vitamin e each day. there are three brands of vitamin supplement available: brand x contains 2, 1, and 2 units, brand y contains 3, 2, and 2 units and brand z contains 4, 4, and 1 units of vitamin a, d, and e, respectively. how many pills of each brand will provide the required amounts of vitamin? pills of brand x, pills of brand y and pills of brand z.

2 pills of brand X, 2 pills of brand Y and 3 pills of brand Z.

Step-by-step explanation:

Required Vitamin :

Vitamin A ⇒ 22 unit

Vitamin D ⇒ 18 unit

Vitamin E ⇒ 11 unit

Units of A,  D,  E per brand :

X            2    1    2

Y            3    2    2

Z             4    4    1

Let 'u' units of X

     'v' units of Y

     'w' units of Z required

Then,

      2u + 3v + 4w  = 22 (1)

      1u  + 2v + 4w  = 18 (2)

     2u  + 2v + 1w  = 11 (3)

By solving the linear equation

u = 2, v = 2, w = 3

2 pills of brand X, 2 pills of brand Y and 3 pills of brand Z.

this is answer of 144 cubic meters