To draw the feasible region, construct table as follows:
| Inequality |
x + 4y ≤ 24 |
3x + y ≤ 21 |
x + y ≤ 9 |
| Corresponding equation (of line) |
x + 4y = 24 |
3x + y = 21 |
x + y = 9 |
| Intersection of line with X-axis |
(24, 0) |
(7, 0) |
(9, 0) |
| Intersection of line with Y-axis |
(0, 6) |
(0, 21) |
(0, 9) |
| Region |
Origin side |
Origin side |
Origin side |
Shaded portion OABCD is the feasible region,
Whose vertices are O(0, 0), A(7, 0), B, C and (0, 6)
B is the point of intersection of the lines 3x + y = 21 and x+y = 9.
Solving the above equations, we get x = 6, y = 3
∴ B ≡ (6, 3)
C is the point of intersection of the lines
x + 4y = 24
and x + y = 9.
Solving the above equations, we get
x = 4, y = 5
∴ C ≡ (4, 5)
Here, the objective function is Z = 3x + 5y,
