With this applet you can investigate linear programming by graphs. You can use the four sliders on the left and the buttons at the bottom to change the constraints of the problem.
Checking the "Objective function" box at the top enables you to change and see the objective function. So you can investigate the maximum value of the objective function subject to the constraints.

Clicking the button "Integer points of the feasible region" shows small circles representing integer points on the graph.
By playing around you can get a good idea of linear programming techniques so that when you come to draw them for yourself you'll know what to do. Enjoy and have fun as you practise an important skill.