The minimum value of the objective function z = 60a + 50b is 370
How to find the minimum value of the objective function
From the question, we have the following parameters that can be used in our computation:
z = 60a + 50b
Subject to the constraints:
10a + 20b ≤ 200
8a + 5b ≤ 80
a ≥ 2, b ≥ 5
The graph of the constraints is added as an attachment
From the graph, we have the following feasible points
(a, b) = (2, 5), (2, 9), (5.5, 7.3) and (6.9, 5)
Recall that
z = 60a + 50b
So, we have
z = 60 * 2 + 50 * 5 = 370
z = 60 * 2 + 50 * 9 = 570
z = 60 * 5.5 + 50 * 7.3 = 695
z = 60 * 6.9 + 50 * 5 = 664
Hence, the minimum value of the objective function is 370