Final answer:
The solution to the minimization problem is found by using linear programming to graph the constraints, forming a feasible region. The minimum value of the objective function C is obtained by evaluating it at the vertices of this region.
Step-by-step explanation:
To solve the minimization problem given by minimize C = -2x + y, subject to the constraints x + 2y ≤ 48, 3x + 2y ≤ 96, x ≥ 0, and y ≥ 0, we can use the method of linear programming, specifically the graphical solution approach.
First, we graph the constraints on a coordinate plane, creating a feasible region where all conditions are satisfied simultaneously. The objective function C must be minimized within this feasible region. To find the optimal solution, we locate the vertex of the feasible region that gives the smallest value for C. This would typically involve evaluating C at all corner points of the feasible region defined by the intersection of the constraints.
Once the minimum value of C is found at a specific point (x, y), this will be the solution to the problem with C representing the minimum cost. Without the actual graph or further computational results presented, we cannot provide the exact minimum value or the point at which this minimum occurs.