Separate the initial or "objective" equation from the constraints. This will help you get a better understanding of what the problem requires and exactly what you are dealing with in the problem.
Write out all of the equations on a piece of paper. Make sure to separate the constraints from the objective equation.
Solve all of the constraints for one variable. Put the solution variable on the right side of the equations and the other variables and constants on the left side.
Draw a graph using the variable you solved for as the vertical axis and the other variable as the horizontal axis; traditionally the "y" variable is on the vertical axis. The vertical line is the dependent variable and the horizontal line is the independent variable. Once you have solved each constraint for a specific variable, each equation will represent a line.
Choose an arbitrary number and substitute it for the independent variable in one of the constraint equations. Solve the equation.
Use the point you chose along with the solution to the equation to plot a point on the graph. The two values will comprise an ordered pair. Choose another number and solve the equation to plot another point.
Connect the two points in a straight line. The line is a representation of the equation.
Shade the area of the graph that corresponds to the constraint. For example, if the initial constraint was on all points greater than the equation, shade all points above the line on the graph.
Plot two points for each of the other equations, draw their corresponding lines and shade the constrained area. Alternatively, you can use a graphing calculator to graph each line. The unshaded area of the graph is the set of all possible solutions, or the solution set.
Look at the graph and determine which lines intersect. Each point of intersection will appear as a vertex on the solution set. Vertexes connected by line segments will surround the solution set. When two lines intersect, they form one of these vertexes.
Set the constraint equations of the two lines that comprise a vertex equal to each other. Combine all like terms and solve the equation for the independent variable. Substitute the solution into one of the two equations to get the dependent variable; together they make up the coordinates of the point at which both lines intersect. Repeat the process for each vertex and write down all of the ordered pairs.
Substitute each pair of points into the objective equation and solve. The solution with the largest numerical value is the maximum output for the problem, given the established constraints.