Math Is Fun Forum

Prakash Panneer

Member

Registered: 2006-06-01

Posts: 110

Matrix help me...........

John takes a daily prescription composed of 8 units of A, 14 units of B, and 16 units of C. The generic drug capsules that contain these ingredients of each of these components is shown below. How many capsules of each drug should John take daily?

         Generic I Generic II Generic III Requirements
A             2            1              3             8 units
B             3            2              5           14 units
C            2             4              2           16 units

---

Letter, number, arts and science
of living kinds, both are the eyes.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Matrix help me...........

We can get three simultaneous equations from this:

2x + y + 3z = 8           [1]
3x + 2y + 5z = 14        [2]
2x + 4y + 2z = 16        [3]

(where x, y and z are the amount of I, II and III respectively that he should take.)
Now we need to combine these equations to eliminate some variables.

2*[2] - 3*[1] --> y+z = 4  [4]
[3]-[1] --> 3y - z = 8.       [5]

Now we have reduced the problem into 2 simultaneous equations with 2 variables. We can reduce this further:
[4]+[5] --> 4y = 12 --> y = 3.

From this, we can use either [4] or [5] to find z, which turns out to be 1.
Then using y and z, we can find x using [1], [2] or [3].
For example, using [1] gets that 2x + 3 + 3*1 = 8 --> 2x = 2 --> x=1.

Therefore, John should take 1 of drug I, 3 of drug II and 1 of drug III.

---

Why did the vector cross the road?
It wanted to be normal.