Step 1:

Let $x$ be the no of sweaters of type A and y be the no of sweaters of type B.

It is given that it costs Rs 360 to make type A and Rs120 to make type B.

It can spend at most of Rs72000 per day.

$\therefore 360x+120y\leq 72000$

$\Rightarrow 3x+y\leq 600$

It is given that the company can product at most of 300 sweaters of both type per day.

$\therefore x+y\leq 300$

It is also given that type B no of sweater cannot exceed no of type A sweater by more than 100.

$\therefore y-x\leq 100$

The company makes a profit of Rs200 of type A sweaters and Rs 120y for type B sweater.

Hence to maximize the profit,the objective function $Z=200x+120y$

Step 2:

Now let us draw the graph for the lines

$AB :3x+y=600,CD :x+y=300$ and $EF :y-x=100$

Consider the line $AB :3x+y=600$

Put $x=0,y=0$ then $0\leq 600$ is true.

Hence the region $3x+y\leq 600$ lies below the line AB.

Consider the line $CD :x+y=300$

Put $x=0,y=0$ then $0\leq 300$ is true.

Hence the region $x+y\leq 300$ lies below the line CD.

Consider the line $EF :y-x=100$

Put $x=0,y=0$ then $0\leq 100$ is true.

Hence the region $y-x\leq 100$ lies below the line EF.

The feasible region OXPQB is the shaded portion shown in the fig.

The coordinates of $P$ is (100,200)

The coordinates of $Q$ is (150,150)

The corner points are $O(0,0),X(0,100),P(100,200),Q(150,150),B(200,0)$

Step 3:

Let us obtain the values of the objective function $Z=200x+120y$

At the points $(x,y)$ the value of the objective function subjected to $Z=200x+120y$

At $O(0,0)$ the value of the objective function $Z=0$

At $X(0,100)$ the value of the objective function $Z=200\times 0+120\times 100=12000$

At $P(100,200)$ the value of the objective function $Z=200\times 100+120\times 200=20000+24000=44000$

At $Q(150,150)$ the value of the objective function $Z=200\times 150+120\times 150=30000+18000=48000$

At $B(300,0)$ the value of the objective function $Z=200\times 300+0=60000$

The maximum profit is at $Rs.48000$ at $Q(150,150)$

Hence 15 sweaters of each sweater should be produced for a maximum profit of Rs.48,000