Features of Linear Programming Problems
 There are 2 quantities that need to be determined.
Each quantity is represented by a variable.
 The problem states conditions about those quantities
that can be represented using linear inequalities (or
equations) in those variables
 There is a particular linear function in those variables
that is to be maximized or minimized (i.e. profit
equation)
 The task is to find the values for the 2 variables that
maximize or minimize the linear function while
satisfying the constraints
Strategy for solving
1. Write the constraints as a set of linear inequalities
(including inequalities that state the variables are
non-negative
2. Graph each inequality and find where their graphs
overlap, i.e. the feasible region
3. Draw one or more profit lines that represent the
function that is to be maximized or minimized
4. Determine where in the feasible region the profit
function will have its maximum or minimum by
seeing where the family of parallel profit lines
leaves the feasible region.
5. Identify the coordinates of the point you found in
step #4.
687315854
Strategy for solving w/out graphing
1. Write the constraints as a set of linear inequalities
(including inequalities that state the variables are
non-negative
2. Find all points where boundary lines intersect by
solving all possible pairs of linear equations
corresponding to the constraints
 These are the intersection points or corner
points
3. Write down the function being minimized or
maximized
4. Evaluate this function at each of the intersection
points found in step #2 and determine which gives
the minimum or maximum value that is inside the
feasible region
687315854
Strategy for n-variables
1. List the constraints, both equations and
inequalities, including inequalities that state the
variables are non-negative
2. Make a list of all combinations of constraints, n at a
time, that includes every constraint equation.
3. For every combination, look for a common solution
to the corresponding system of linear equations.
 If there is a unique solution, then this is a
“potential” corner point.
 If there is no unique solution, then ignore the
point.
4. Test all “potential” corner points to make sure they
fit all the constraints. Those that do become
“actual” corner points.
5. Evaluate the profit function at these “actual” corner
points.
6. Identify the point that maximizes or minimizes your
profit function.
687315854