Step 1:

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.

Step 2:

The mathematical formulation is as follows :

Maximize $Z=30x+25y$

Subjected to $3x+3y\leq 18$ and $3x+2y\leq 15$ and $x,y\geq 0$

Here $Z$ denotes the maximum profit.

Step 3:

To solve this LPP graphically let us convert the inequalities into equation and draw the corresponding lines.

$3x+3y=18$

$x+y=6$

$3x+2y=15$

Clearly OAPC is the feasible region which is shaded.

The corner points are $O(0,0),A(5,0),P(3,3),C(0,6)$

Step 4:

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.