It is given that
Z = 3x + 5y, subject to the constraints
x + 2y ≤ 2000, x + y ≤ 1500, y ≤ 600, x ≥ 0 and y ≥ 0
Draw the line x + 2y = 2000, x + y = 1500 and y = 600 and shaded region which is satisfied by above inequalities
We know that the feasible region is bounded
O (0, 0), A (1000, 500), B (800, 600), C (0, 600) and D (1500, 0) are the corner points
So the value of Z at O (0, 0)
Z = 0
Value of Z at A (1000, 500)
Z = 5500
Value of Z at B (800, 600)
Z = 5400
Value of Z at C (0, 600)
Z = 3000
Value of Z at D (1500, 0)
Z = 4500
Hence, the maximum value of Z is 5500 which occurs at A (1000, 500).