The maximum value of the objective function is 9.65 at the feasible point (1.47, 2.62)
How to find the maximum value of the objective function
From the question, we have the following parameters that can be used in our computation:
Max z = 3x + 2y
Subject to:
5x + y ≥ 10
10x + y ≥ 6
x + 4y ≥ 12
Plot the graph of the constraints (see attachment)
From the graph, we have the feasible coordinates to be
(x, y) = (0.31, 2.92) and (1.47, 2.62)
Recall that
Max z = 3x + 2y
So, we have
z(0.31, 2.92) = 3 * 0.31 + 2 * 2.92 = 6.77
z(1.47, 2.62) = 3 * 1.47 + 2 * 2.62 = 9.65
The maximum of these values is 9.65
Hence, the maximum value of the objective function is 9.65