Given linear programming is
Max C = 3x + 5y
subject to x \(\leq\) 1
2y \(\leq\) 12 ⇒ y \(\leq\) 6
3x + 2y = 18
x \(\geq\) 0, y \(\geq\) 0
feasible region of given lpp is the points of region (x \(\leq\) 4 & y \(\leq\) 6, i.e., rectangular field ABCD)
Which satisfies the equation 3x + 2y = 18.
By drawing graph, we observed that line segment of line 3x + 2y = 18 joining point (2, 6) and (4, 3) is feasible region of given lpp whose corner points is (2, 6) and (4, 3)
Check the value of objective function at corner points, we get
| Corner Points |
Objective function C = 3x + 5y |
| (2, 6) |
6 + 30 = 36 |
| (4, 3) |
12 + 15 = 27 |
\(\therefore\) Maximize of C occurs at (2, 6) and maximum value of 36.
