Plot the straight lines 12x+4y=60

Consider (shade) the region between this line and the origin of the graph paper, 4x+8y=40

consider (shade) the region between thisline and the origin of the graph paper

The region common for the two above is the critical region and one of its vertices give the maximum profit.The vertices of the critical region are:

(0, 0) with unused 60 hours ofline 1 and 40 hours of Line 2, NSK (0, 5), with unused 40 hoursof line 1 ,

(4, 3) with no unused resources. as (4, 3) represents 4 units of product A and 3 units of product B which utilizes 12*4+4*3=60 hours of Line 1 and 4*4+8*3=40 hours of Line 2.

and (5,0) with unused 20 hours of Line 2

The profit function is P=9x+7y

P is maximum at (4,3)

In the part (b) of the problem the line (1) will be 12x+4y=40