Question

A company manufacturers toys of three brands A, B and C. Average number of
toys manufactures per day by Three types of employees I, II and III are 14, 16,
and 10 respectively
The mean daily production of the toys being 196 toys . two days due to strike only
1/4 of the II type of employees and III type of employees and 1/2 of the I type of
employees attended the job and only 50 toys were manufactured . Find the
number of employees of each type in the company, the total number of
employees were 46. solve this question by Matrix inversion and give the reason
why we solve this question by Matrix inversion​

Answer 1

Given :  A company manufacturers toys of three brands A, B and C. Average number of  toys manufactures per day by Three types of employees I, II and III are 14, 16,  and 10 respectively

The mean daily production of the toys being 196 toys

To Find : the  number of employees of each type in the company,

Solution:

Three types of employees I, II and III  are X  , Y  & Z  respectively

X + Y  + Z   = 46

14X + 16Y + 10Z  = 196  => 7X + 8Y + 5Z  = 98

14X/2 + 16Y/4 + 10Z/4  = 50/2

=> 14X + 8Y + 5Z  =  100

X + Y  + Z   = 46    Eq1

7X + 8Y + 5Z  = 98   Eq2

14X + 8Y + 5Z  =  100   Eq3

Eq3 - Eq2  => 7X = 2  => X = 2/7

Mistake in data  as people can not be in fraction

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