x and y will represent quantities of two commodities, and an objective function is a function that we want to maximise or minimise (depending on the context of the question, you might want to maximise profits, or you might want to minimise costs or time taken to complete a project, for example) from these commodities. But this will depend on certain constraints.
The constraints will be drawn as linear inequalities, which together give a feasible region.
The most important thing to remember is that linear functions reach their maximum or minimum at their endpoints. The endpoints of these linear inequalities are at the corner points.
So you need to evaluate the objective functions at each of the corner points (i.e. substitute each corner point into the objective functions), and see which corner points give you the maximum and minimum values, and of course, what those maximum and minimum values are.
See how you go.