Machines |
Toys |
I |
II |
III |
Profit |
A(x) |
12 |
18 |
6 |
Rs. 7.50 |
B(y) |
6 |
0 |
9 |
5 |
Maximize
z = \(\frac{15}{2}\)x + 5y
subject to the constraints
(i) 12x + 6y ≤ 360
⇒ 2x+y ≤ 60
(ii) 18x ≤ 360 ⇒ x ≤ 20
(iii) 6x + 9y ≤ 360
⇒ 2x +3y ≤ 120
(iv) x ≥ 0 , y ≥ 0
ABCDE is the solution region
A (0, 0) Z = 0
B (20, 0) Z = Rs 150
C (20, 20) Z = Rs 250
D (15, 30) Z = Rs 262.5 ,
E (0, 40) Z = Rs 200
At D (15, 30) Z is maximised to Rs 262. 5