Question

A firm manufactures pain relieving pills in two sizes A and B. Size A contains 4 grains of element X, 7 grains of element Y, and 2 grains of element Z. Size B contains 2 grains of element X, 10 grains of element Y and 8 grains of element Z. It is found by users that it requires at least 12 grains of element X .74 grains of element Y, and 24 grains of element Z to provide immediate relief. It is required to determine the least number of pills a patient should take to get a immediate relief. Formulate the LPP and find the solution.

Answer 1

Given :   Size A contains 4 grains of element X, 7 grains of element Y, and 2 grains of element Z.

Size B contains 2 grains of element X, 10 grains of element Y and 8 grains of element Z.

To find : least number of pills a patient should take to get a immediate relief

Solution:

Let say size  A pils  = x

Size B pills = y

x ≥ 0 , y ≥ 0

4x + 2y ≥ 12 => 2x  + y  ≥ 6

7x + 10y ≥ 74

2x + 8y ≥ 24  => x + 4y  ≥ 12

Z = x + y  minimum

From graph 3  points

( 0 , 7.4)

(88/9 , 5/9)

(12 , 0)  

Minimum is at  (0 , 7.4)

but tablets has to be in integer form

Hence ( 0 , 8) or ( 1, 7)

Least number of pills = 8

Learn More:

Shalmali wants to invest ₹50,000 in saving certificates and PPF ...

https://brainly.in/question/6332423

Old hens can be bought at rs. 2 each and young ones at rs. 5 each ...

https://brainly.in/question/9077084

Answer 2

i give my solution......