It is given that
Z = 4x + 9y, subject to the constraints
x ≥ 0, y ≥ 0, x + 5y ≤ 200, 2x + 3y ≤ 134
Draw the line x + 5y = 200 and 2x + 3y = 134 and shaded region which is satisfied by above inequalities
We know that the feasible region is bounded
O (0, 0), A (10, 38), B (67, 0) and C (0, 40) are the corner points
So the value of Z at O (0, 0)
Z = 0
Value of Z at A (10, 38)
Z = 382
Value of Z at B (67, 0)
Z = 268
Value of Z at C (0, 40)
Z = 360
Hence, the maximum value of Z is 382 which occurs at A (10, 38).