Let x and y be number of deluxe article manufactured and ordinary article manufactured.
∴According to the question,
2x + y ≤ 40, 2x + 3y ≤ 80, x ≥ 0, y ≥ 0
Maximize Z = 15x + 10y
The feasible region determined by 2x + y ≤ 40, 2x + 3y ≤ 80, x ≥ 0, y ≥ 0 is given by
The corner points of feasible region are A(0,0) , B(0,80/3) , C(10,20),D(20,0).
The value of Z at corner points are
Corner Point |
Z = 15x + 10y |
|
A(0, 0) |
0 |
|
B(0, 80/3) |
266.67 |
|
C(10, 20) |
350 |
Maximum |
D(20, 0) |
300 |
|
The maximum value of Z is 350 at point (10,20).
Hence, the manufacturer should produce 10 types of deluxe article and 20 types of ordinary article to make maximum profit of Rs.350.