Final answer:
The function f(x,y,z) has constraints which can be used to express it in terms of a single variable, x, but due to insufficient constraints, exact maxima and minima cannot be determined with the mismatching information provided.
Step-by-step explanation:
To find the maximum and minimum of the function f(x,y,z)=2x+y-z, given the constraints 2x+z=2/√5 and y²/4=1, we can use the method of Lagrange multipliers or solve the constraints directly to find feasible points. Since y²/4=1 implies y=±2, we can substitute this into the function. Also, substituting the value of z from 2x+z=2/√5 into the function gives us a new function of x only, which we can differentiate to find extrema.
After substitutions and simplifications, we may analyze the critical points and evaluate the function to find the maximum and minimum values under the given constraints. However, due to mismatching information in the provided context and no precise constraint on x, an exact solution is not obtainable with the given data. Should additional constraints or corrections be provided, we can proceed with a precise calculation.