Question

A company manufactures two types of TV sets, which are assembled and finished in two workshops W1 and W2. Each type takes 20 hours and 10 hours for assembly and 5 hours and 3 hours for finishing in the respective workshops. If total number of hours available are 450 and 230 in workshops W1 and W2 respectively, Calculate the number of units of each type be produced, using matrix method only.

Answer 1

The number of units of each type be produced are 20 and 10 respectively.

Step-by-step explanation:

We are given that a company manufactures two types of TV sets, which are assembled and finished in two workshops W1 and W2. Each type takes 20 hours and 10 hours for assembly and 5 hours and 3 hours for finishing in the respective workshop.

The total number of hours available is 450 and 230 in workshops W1 and W2 respectively.

Let the number of units produced of W1 be 'x' and the number of units produced of W2 be 'y'.

So, according to the question;

       $\left[\begin{array}{cc}20&5\\10&3\end{array}\right] = \left[\begin{array}{c}450&230\end{array}\right]$

Here 20 hours of assembling and 5 hours of finishing belongs to workshop W1 and 10 hours of assembling and 3 hours of finishing belongs to workshop W2.

450 is the total number of hours available in workshops W1 and 230 is the total number of hours available in workshops W2.

Now, this represents that;

$20x+5y=450$    and    $10x + 3y = 230$  

$4x+y=90$

$y = 90-4x$  ------------- [equation 1]

Now, substituting the value of y in the second equation we get;

$10x + 3\times(90-4x) = 230$

$10x + 270-12x = 230$

$270-2x = 230$

$2x= 270-230$

$x =\frac{40}{2}$ = 20

Now, putting the value of x in equation 1 we get;

$y = 90-4x$

$y = 90-(4 \times 20)$

$y =90-80$ = 10

Hence, the number of units of each type be produced are 20 and 10 respectively.