We are given 42h or machine time and 24h of craftsmen time. Let x be the number of tennis rackets and y be the number of cricket bats that we can make. Our problem is to find out the maximum profit at full capacity.
Clearly, x, y ≥ 0. Let us construct the following table from the given data.

Tennis Rackets (x) 
Cricket Bats (y) 
Requirements 
Machine Time (h) 
1.5 
3 
42 
Craftsmen Time (h) 
3 
1 
24 
Profit (Rs) 
20 
10 

Since we have only 42h of machine time and 24h of craftsmen time, we have to maximize x+y, given the following constraints:
$(1): 1.5x + 3y \leq 42$
$(2): 3x + y \leq 24$
$(3): x \leq 0, \; (4): y \leq 0$
$\textbf{Plotting the constraints}:$
Plot the straight lines 1.5x + 3y = 42 and 3x + y = 24
First draw the graph of the line 1.5x + 3y = 42. If x = 0, y = 14 and if y = 0, x = 28. So, this is a straight line between (0,14) and (28,0).
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 3x + y = 24. If x = 0, y = 24 and if y =0, x = 8. So, this is a straight line between (0,24) and (8,0).
At (0,0), in the inequality, we have 0 + 0 = 0 which is ≤ 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 1.5x + 3y = 42 and 3x + y = 24, we get,
1.5x + 3 (243x) = 42 $\to$1.5x + 72 – 9x = 42 $\to$7.5x = 30 $\to$x =4 .
If x = 4, y = 24 – 12 = 12.
$\Rightarrow x = 4, y = 12$
Therefore the feasible region has the corner points (0,0), (0,14), (4,12), (8,0) 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 = 20x + 10y

O (0,0)

0

A (0,14)

160

E (4,12)

200 (Maximum value)

B (8,0)

140

$\textbf{A) The number of rackets and bats we can make at full capacity are 4 and 12. }$
$\textbf{B) The maximum profit we can make that meet the constraints is 200. }$