Final answer:
The student aims to find the minimum and maximum values for an objective function with given constraints using linear programming. Due to possible missing information in the constraints provided, the exact solution cannot be determined without clarification. Generally, this involves graphing the constraints, identifying the feasible region, and evaluating the objective function at its vertices.
Step-by-step explanation:
The student is seeking to find the minimum and maximum values of the objective function z = 9x + 5y given a set of constraints. This type of problem is often solved using linear programming methods, which involve graphing the constraints and finding the feasible region. The maximum and minimum values for the objective function occur at the vertices of the feasible region. However, based on the information provided, it seems there might be missing or incorrect constraints, as typical constraints are inequalities. Assuming the inequalities given should be interpreted as 5x + 4y ≥ 20, x + 4y ≥ 28, and x ≥ 0, y ≥ 0, we would first graph these inequalities, find the vertices of the feasible region, and then evaluate the objective function at each vertex to find the minimum and maximum values.