Let the number of rackets made = x and that of bats = y.
Maximise; Z = x + y
Machine constraints 1.5x + 3y ≤ 42
Craftsman’s constraint 3x + y ≤ 24
Therefore; Maximise; Z = x + y
x + 2y ≤ 14, 3x + y ≤ 24, x ≥ 0, y ≥ 0
In the figure the shaded region OABC is the fesible region. Here the region is bounded. The
corner points are O(0, 0), A(8, 0), B(4, 10), C(0, 14).
Given; Z = x + y
Corner points |
Value of Z |
O |
Z = 0 |
A |
Z = 8 + 0 = 8 |
B |
Z = 4 + 12 = 16 |
C |
Z = 0 + 14 = 14 |
Since maximum value of Z occurs at B, the solution is Z = 16, (4, 12).