the variable you want to maximise or minimise (P) = each variable times the amount of P the contribute e.g. maximise money earned x=£3 y=£2.50 z=£4 (MAX)P=3x+2.5y+4z is the objective function
Linear programming is just graphing a bunch of linear inequalities.
Remember that when you graph inequalities, you need to shade the "good" region - pick a point that is not on the line, put it...
A feasible region is, in a constrained optimization problem, the set of solutions satisfying all equalities and/or inequalities. On the other hand a linear programming is a constrained optimization...