Linear Programming on the Graphing Calculator
1.
Start with the Y= button to enter
your equations. You will want to tell
the calculator that you want to do an
inequality. Arrow over to the left until
the diagonal line next to Y1 begins to
blink.
3.
To enter your equations,
you must first arrow back to the
right until you are to the right of
the equals sign. Enter the two
variable inequalities only.
Next we are going to graph.
How do I know what to change my x and y min and
maxes to so that I get a graph that makes sense???
2.
Now press enter. The
blinking cursor will change. If
you are graphing a greater than
function (y > x) you want your
screen to look like this, with a
right triangle in the upper right
corner.
Press ENTER again and the
triangle will go to the lower left
corner. This is the less than
function (y < x). Depending on
your equation you will want one
of the two of these two cursors to
be blinking.
If you start with ZOOM and select 6 (ZStandard) you
will get a typical X, Y coordinate graph. Notice here
we do not have a good overlapping boundary. Play
with the window settings and find a min and max for
your X and Y values that will give you a boundary
that looks good. For this problem, I have given you
the values that will work.
4.
Press the WINDOW button.
You want to change minimum and
maximum settings of the x and y. Make
0 < x < 12 and 0 < y < 20
5.
Pressing GRAPH your
screen should now look like
this:
6.
Use the option to get
the left vertex intercept. To do
this, press 2ND and CALC
(above the TRACE key).
Arrow down to 2: zero and
press ENTER.
8.
2ND MODE will
quit and get you back to
the home screen.
Clear any equations or
number that you may have
here and enter the
Objective Function (P). In
this example we will use
the function P = 13X + 2Y
7.
Your graph will now have
an equation at the top left of the
screen; this is the one of the
boundaries we inputted originally.
Note: Notice the X=6 in the left
hand part of the screen. We want
the blinking cursor to be at X=0.
Use the left arrow key to move the
cursor down to the axis until X=0.
Your screen should look
like this.
You will use the variable
button to input X but in
order to input Y, you will
need to press ALPHA and
then 1. This will give you
your Y in the equation.
9.
Press ENTER. This will
give you the value of P at the
vertex. In this case it is 8.
10.
Go back to the CALC
function, above the TRACE
button (2ND, TRACE). Select
5:intersect and press ENTER for
the value of P
12.
Go back to the home
screen (2ND, MODE). Press
ENTER. You will now get
the maximum value of the
objective function when the
constraint point (8, 16) on
the intersecting graphs is
analyzed.
In other words, the maximum value of 136 occurs when x = 8 and y = 16.
More Practice:
11.
The calculator will now ask
you a series of questions. Press
ENTER for each question.
First curve?
Second curve?
Guess?
You want your screen to look like
this, so that the Intersection is the P
value that was calculated in Step 9.
(Press Enter)
(Press Enter)
(Press Enter)
Find the values of x and y that maximize or minimize the objective function.
Practice 1:
4x + 3y > 30
Hint: solve for y for the 1st two
x + 3y >21
equations 1st.
x> 0 , y >0
Minimum for C = 5X+8Y
Answer: 3,6 C=36
Your graph should look like this:
Practice 2:
3x + 5y < 35
2x + y < 14
x>0, y>0
Maximum for P = 3x + 2y
Answer: 5,4; P = 23
Your graph should look like this: