The data given in the problem can be summarized as follows :
Let $x$ units of type A and y units of type B be produced to fulfill the requirement.
The mathematical formulation is as follows :
Subjected to $3x+3y\leq 18$ and $3x+2y\leq 15$ and $x,y\geq 0$
Here $Z$ denotes the maximum profit.
To solve this LPP graphically let us convert the inequalities into equation and draw the corresponding lines.
Clearly OAPC is the feasible region which is shaded.
The corner points are $O(0,0),A(5,0),P(3,3),C(0,6)$
Now let us obtain the values of Z as follows :
At the points $(x,y)$ the value of the objective function subjected to $Z=30x+25y$
At $O(0,0)$ the value of the objective function $Z=0$
At $A(5,0)$ the value of the objective function $Z=30(5)+25(0)=150$
At $P(3,3)$ the value of the objective function $Z=30(3)+25(3)=165$
At $C(0,6)$ the value of the objective function $Z=30(0)+25(6)=150$
Clearly $Z$ has maximum value of 165 at the point $P(3,3)$
Hence 3 trunks of each type is required to be produced to obtain maximum profit.