P = 5x + 6y
subject to the constraints
(i) 5x + 8y ≤ 200
(ii) 10x + 8y ≤ 240
⇒ 5x + 4y ≤ 120
(iii) x ≥ 0; y ≥ 0
A (0,0) P = 5x + 6y = 0
B (24,0) P = 5 x 24+ 6 x 0= 120 Rs
C (8,20) P = 5 x 8 + 6 x 20 = 160 Rs
D (0, 25) P = 5 x 0+ 6 x 25 = 150 Rs
At C (8, 20) P is maximised to Rs 160
∴ 8 types of A and 2 : 6 types of B