Question

Two tailors A and B earn Rs 150 and Rs 200 per day respectively. A can stitch 6 shirts and 4 pants per day while B can stitch 10 shirts and 4 pants per day. Form a linear programming problem to minimize the labour cost to produce at least 60 shirts and 32 pants.

Answer 1

Let tailor A work for x days and tailor B work for y days.
In one day, A can stitch 6 shirts and 4 pants whereas B can stitch 10 shirts and 4 pants.
Thus, in x days A can stitch 6x shirts and 4x pants. Similarly, in y days B can stitch 10y shirts and 4y pants.

It is given that the minimum requirement of the shirts and pants are respectively 60 and 32 respectively.

Thus,

$$\begin{gathered} 6x+10y\ge 60 \\ 4x+4y\ge 32 \end{gathered}$$

Further it is given that A and B earn Rs 150 and Rs 200 per day respectively. Thus, in x days and y days, A and B earn Rs 150x and Rs 200y respectively.

Let Z denotes the total cost

$\therefore \mathrm{Z}=\mathrm{Rs}\left(150x+200y\right)$

Number of days cannot be negative.
Therefore, $x,y\ge 0$

Hence, the required LPP is as follows:
Minimize $\mathrm{Z}=150x+200y$

subject to

$$\begin{gathered} 6x+10y\ge 60 \\ 4x+4y\ge 32 \\ x\ge 0,y\ge 0 \end{gathered}$$