Step 1:

The information given can be tabulated as follows :

Now we can mathematically formulate the above information as follows :

The objective function $z=510x+675$ subjected to constraints $x+y\leq 300$

$1800x+2700y\leq 6,48,000$

$x,y \geq 0$

Step 2:

Let us plot the lines in the graph to obtain the feasible region and the corner points.

Clearly the shaded portion is the feasible region .The corner points are O(0,0),A(300,0),B(180,120),C(0,240)

Step 3:

Now let us find the value of the objective function $z=510x+675y$

At the points $(x,y)$ the value of the objective function subjected to $z=510x+675y$

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

At $A(300,0)$ the value of the objective function $Z=510\times 300+675\times 0=153000$

At $B(180,120)$ the value of the objective function $Z=510\times 180+675\times 12 0=172800$

At $C(0,240)$ the value of the objective function $Z=510\times 0+675\times 240=162000$

Clealy $z$ has maximum value at $B(180,120)$

Hence 180 sets of black and white TV sets and 120 sets of color TV sets should be manufactured to obtain a maximum profit.