Unit 8 - linear programming 2
3.3 Graphing the Objective Function
The optimum occurs at a corner point of the feasible region
If you want to, you can use the Linear Programming Solver to check your solutions.
Open the Solver, click on Show Example and enter your problem in standard form.
Activity 1
The applet below shows the feasible region (shown in yellow) for the constraints
x+y <= 4
2x-y >= 2
x <= 3
y >= 0
It also shows the graph of the Objective function (magenta)
P = 3x + 2y
and a point P(x, y) on the graph.
Click on the Px and/or Py arrows to move point P(x, y). You can also click-hold-and-drag point P or type values for Px and Py. As the values of x and y change, the value of the objective function P = 3x+2y changes - the value of the Objective function is displayed in blue, and he graph for each new value is also displayed.
Explain: Why are the lines for different values of the Objective function parallelel?
Investigate: How does the value of the Objective function change as it "moves"?
For what values of x and y in the feasible region is the Objective function a maximum, and what is the maximum?
For what values of x and y in the feasible region is the Objective function a minimum, and what is the minimum?
Note: Press "Clear" to clear traces. If the applet becomes smudged, click "init" (initialise).
applet 81
applet 82
The applet below shows the same feasible region, but the Objective function is now
P = x + 2y
What is now the maximum and what is the minimum value of P?
Explain why the solution is different from Activity 1!
applet 83
The applet below shows an unbounded feasible region with Objective function
P = 2x+3y
Find the maximum feasible and minimum feasible values of the Objective function by dragging P, or clicking the Px and Py arrows or typing values for Px and Py.
Activity 4: LPSolverObjective.htm
Click here for LINEAR PROGRAMMING SOLVER
Click here for to download the embedded HELP file
Activity 5: LPSolverBus.htm
Click here for LINEAR PROGRAMMING BUS SOLVER
WRAP-UP
LPSolverLunch.htm
Click here for LINEAR PROGRAMMING LUNCH SOLVER