Final answer:
The function provided, z = 4x + 3yx + 5y, appears to contain a typo making it non-linear, which is not standard for a linear programming problem. Assuming a typo and a linear function was intended, one would graph the constraints, find the feasible region, and test the objective function's value at each vertex to find the maximum, which cannot be determined from the information given.
Step-by-step explanation:
The goal is to maximize the function z = 4x + 3yx + 5y under the given constraints 4x + 2y ≤ 28, x ≥ 0, and y ≥ 0. To solve this linear programming problem, you typically use graphical methods or simplex algorithm when working with more complex problems. However, this function to maximize seems to be incorrect as it contains a product of variables (xy), making it a non-linear function, which is not typically the case in linear programming. There could potentially be a typo in the original function. Assuming that the function was intended to be linear and was a typo, and the correct function is z = 4x + 3y, you would still graph the constraints, identify the feasible region, and find the value of the objective function at each vertex of the feasible region to locate the maximum value. Without the correct function, the maximum cannot be determined.