Final answer:
To solve the given LP formulation, first, graph the feasible region determined by the given constraints. Then, find the vertices of the feasible region and evaluate the objective function at each vertex. The maximum profit occurs at the vertex with the highest objective function value.
Step-by-step explanation:
To solve the given linear programming problem, first, we need to graph the feasible region determined by the given constraints.
The constraints are:
- 1x + 1y ≤ 5 (Constraint A)
- 1x ≥ 2 (Constraint B)
- 2y ≤ 8 (Constraint C)
- x ⋅ y ≥ 0 (Constraint D)
Plotting these constraints on a graph, we find that the feasible region is a triangle bounded by the lines x = 2, y = 0, and y = 4.
Next, we need to find the coordinates of the vertices of this feasible region. The vertices are (2,0), (2,4), and (5,0).
Finally, we evaluate the objective function 3x + 2y at each vertex:
- At (2,0), 3(2) + 2(0) = 6.
- At (2,4), 3(2) + 2(4) = 14.
- At (5,0), 3(5) + 2(0) = 15.
The maximum profit occurs at the vertex with the highest objective function value, which is (5,0), with a profit of $15.