Maximize Z = 2x + 3y
We rewrite the constraints as equalities to determine their boundary lines:
These constraints, along with x ≥ 0 and y ≥ 0, define the feasible region.
We determine the vertices by solving the equations pairwise.
Solving:
Vertex: (40/13, 15/13)
Solving:
Vertex: (4/3, 4/3)
Solving:
Vertex: (5/7, 18/7)
The maximum value of Z = 64/7 occurs at the vertex (5/7, 18/7).
Given the Linear Programming Problem:
Maximize \( z = 11x + 7y \) subject to the constraints: \( x \leq 3 \), \( y \leq 2 \), \( x, y \geq 0 \).
Then the optimal solution of the problem is: