Our problem is to maximize Z = 5x + 3y …(i)
Subject to constraints 3x + 5y ≤ 15 …(ii)
5x + 2y ≤ 10 (iii)
x ≥ 0, y ≥ 0 …(iv)
Firstly, draw the graph of the line 3x + 5y = 15
Secondly, draw the graph of the line 5x + 2y = 10
On solving given equations 3x + 5y = 15 and 5x + 2y = 10, we get x = 20/19 , y = 45/19
∴ Feasible region is OABCO (see the below figure).
The corner points of the feasible region are O(0, 0), A(2, 0), B(20/19, 45/19) and C(0, 3) The values of Z at these points are as follows:
Therefore, the maximum value of Z is 235/19 at the point B(20/19, 45/19).
