**PROCEDURES TI-83P/84 INEQUALITY APP **

**Content: **This document describes how
to solve a linear programming problem with the Inequality App, Inequal.

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**©
2013 Frank Kizer

**
General: **
This
program omits the part of the application that calculates the value of the
objective function and replaces that with the option to either calculate those values by hand

by substituting in the objective function or by using list arithmetic.

**
Procedure: **
Use of
the application will be demonstrated by using the problem that follows.

Find
the maximum of the objective function z=2x +5y, subject to the following
constraints:

3x+2y __<__ 6 (Eq 1a)

-x+2y __<__ 4 (Eq 2a)

x≥0, y≥0

a) First put the two-variable equations in slope-intercept form.

y __<__ -3/2x+3 (Eq 1b)

y __<__ 1/2x+2 (Eq 2b)

b) Enter the right side of those equations opposite Y1 and Y2 respectively and
enter 0 opposite Y3.

c) Set the WINDOW at Xmin = -1, Ymin=-1, Ymax= the largest value of "b" plus a
few units, say 5 in
this problem. Set Xmax at least one unit higher that the value largest value of
the

y-intercept of the
inequalities with a negative slope. Say, three in this case. You might want to
press GRAPH and see if
all of the corner points of the bounded region are on the screen.

**
Now we will enter the inequality signs.
**a) Move the cursor to the sign (either equal or inequality) after Y1. If the
inequality symbols do not
appear at the bottom of the screen, you will need to start the Inequality App.
Do that by pressing

APPS, move the cursor down to Inequal, or Inequalz for the international version, and press ENTER, ENTER. The Y= editor screen should be displayed.

b) Place the cursor on the equal sign opposite Y1 and press ALPHA, F3 (ZOOM). The equal sign should have been replaced by the inequality

c) Do the same for Y2; then opposite Y3, press ALPHA, F5 (GRAPH). The symbol

Figure 1: Completed Y= screen.

d) Now,
move the cursor up to the "X" in the upper left corner and press ENTER. With the
cursor on the
equal sign opposite X1, press ALPHA, F5 (GRAPH) to enter __>__ ; then enter a zero
after that symbol.

Figure 2: Completed X= screen.

e) Press GRAPH to draw and shade the graphs. The screen in Figure 3 should appear.

Figure 3: Graph with feasible region undefined.

f) Press ALPHA, F1, 1 to define the feasible region.

Figure
4: Defined feasible region. Window settings: Xmin = -1; Xmax=3;Ymin=-1; Ymax=5

**If you only want to graph, you may stop here.**

At this time we will find the x- and y-values of the corner points. We will
record the values for the corner points, so that we have the option of either
calculating the value of
the objective

function by
hand or by using the lists.

At first, getting the cursor to move to the location you want may seem a bit
random. But if you remember a few things, you’ll find it quite easy:
The first item in the expression in the upper left

of the screen tells what line
you’re on. For example, Y1∩Y2 tells you you’re on the first line in the Y=
screen. (Some browsers may return an empty square for the intersection
symbol.) You

can use the left and right arrows to move to different points
on that line. If you want to move to line Y2, press the down arrow.
The up and down arrows move up and down according to

the order that the graphs
or axes are listed on the Y= and X= screens. Y= comes before X=.

a) So, press ALPHA, F3 (ZOOM).
If Y1∩Y2 appears in the upper left of the screen, the values x=.5, y=2.25 will be displayed at the bottom of the screen. (See Figure 5).
Record these values for

later use.

b) Press the right arrow to go to the point x=2, y=0.

c) Now, press the down arrow to go back to the intersection point with Y2∩Y1
on the screen. The Y2 in the expression Y2∩Y1 tells you that you’re on line Y2. Press the
left arrow to go to

the point x=0, y=2. Now press the left arrow to go to the last point, x=0,
y=2.

Figure
5: Screen prepared to go to the corner on the x-axis.

**Evaluating the objective function:
Method by Hand:
**At this point you can choose to plug the corner-point values into your
calculator as follows:
2*.5 + 5*2.25; press ENTER and you’ll get 12.25 for the intersection point. Do
the other points

similarly.

**
Method
Using Lists:**

a) Enter the values for x in list L_{1} and the y-values for y in L_{2}.

b) Now, place the cursor over the name for L_{3} and enter the 2, 2nd, L_{1},
+,5, 2nd, _{L}2._{ }

Figure 6: Shows entry for L_{3} before pressing ENTER to do the
calculations.

c) Press ENTER and the objective values will be entered in list L_{3}.

Released:
9/15/12

Last Revised: