Let x be the number of souveniers of type A and y be the number of souveniers of type B that we can make. Our problem is to maximize x and y and the maximum profit at a given capacity.
Clearly, x, y ≥ 0. Let us construct the following table from the given data

Souvenier A (x) 
Souvenier B (x) 
Time 
Cutting Machine (min) 
5 
8 
3 x 60 + 20 = 200 
Assembling (min) 
10 
8 
4 x 60 = 240 
Profits (Rs.) 
5 
6 

We have the following constraints: 5x+8y $\leq$ 200 and 10x+8y $\leq$ 240 $\to$5x + 4y $\leq$ 120
The profit on Souvenir A is Rs. 5 and on Souvenir B is Rs. 6. We need to maximize the profits, i.e. maximize 5x + 3y, given the above constraints.
$\textbf{Plotting the constraints}$:
Plot the straight lines 5x+8y = 200 and 5x+4y = 120
First draw the graph of the line 5x+8y = 200
If x = 0, y = 200/8 = 25 and if y = 0, x = 200/5 = 40. So, this is a straight line between (0,25) and (40,0).
At (0,0), in the inequality, we have 0 + 0 = 0 which is $\leq$ 0. So the area associated with this inequality is bounded towards the origin.
Similarly, draw the graph of the line 5x+4y = 120.
If x = 0, y = 120/4 = 30 and if y =0, x = 120/5 = 24. So, this is a straight line between (0,30) and (24,0).
At (0,0), in the inequality, we have 0 + 0 = 0 which is $\leq$ 0. So the area associated with this inequality is bounded towards the origin.
$\textbf{Finding the feasible region}$:
We can see that the feasible region is bounded and in the first quadrant.
On solving the equations 5x+8y = 200 and 5x+4y = 120, we get,
8y – 4y = 200 – 120 $\to$4y = 80 $\to$y = 20.
If y = 20, x = (1204x20)/5 = 8.
$\Rightarrow x = 8, y = 20 $
Therefore the feasible region has the corner points (0,0), (0,25), (8,20), (0,25) as shown in the figure.
$\textbf{Solving the objective function using the corner point method}$
The values of Z at the corner points are calculated as follows:
Corner Point 
Z = 5x+6y 
(0,0) 
0 
(0,25) 
150 
(8,20) 
160 (Max Value) 
(24,0) 
120 
$\textbf{The maximum profit we can make is Rs. 160, which involves making 8 Type A Souvenirs and 20 Type B Souvenirs. }$