Question

A company manufactures toys of three brands A, B and C Average arbor of toys manufactured per day by Three types of employees I, II and II are 14, 16, od 10 respectively The mean daly production of the toys being 196 toys two days due to strike only 14 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 the the reason why we solve this question by Matrix inversion​

Answer 1

Answer:

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Step-by-step explanation:

Fabricating Hours Finishing Hours  A9 1  B12 3 

Let pieces of type A manufactured per week =x

Let pieces of type B manufactured per week =y

Companies profit function which is to be maximized: Z =80x+120y as shown in the tabular column:

Constraints: Maximum number of fabricating hours =180

Therefore, 9x+12y≤180⇒3x+4y≤60

Where 9x is the fabricating hours spent by type A teacher aids, and 12y hours spent on type B and maximum number of finishing hours =30.

x+3y≤30

Where x is the number of hours spent on finishing aid A while 3y on aid B.

So, the LPP becomes:

Z(maximise)=80x+120y

Subject to 3x+4y≤60

x+3y≤30

x≥0

y≥0

Solving it graphically:

Z=80x+120y at (0,15)=1800

Z =1200 at (0,10)

Z =1600 at (20,0)

Z =960+720 at (12,6)=1680

Maximum profit is at (0,15).

Therefore, Teacher aid A =0

Teacher aid B =15 should be made.