Casio fx9750GII - MISCELLANEOUS FUNCTIONS (Continued); Linear Programming Inequalities and Combinatorics

Example 2a
Problem: Find the feasible region that satises the following
constraints over the domain 0
x 25 and range 0 y 25:
x + y 15 y 6 4x + y 24 x 2 y 2x
Answer: Rearranging to make y the ‘subject’ gives:
y 15 – x y 6 y 24 - 4x x 2 y 2x
Result
Then enter in the constraints and then draw them
F3 F6 F4
Change Y= to Y
1 5 -
X, θ ,T
EXE 6 EXE 2 4 - 4
X, θ ,T
EXE 1 0 0 0
X, θ ,T
- 2 0 0
0 EXE 2
X, θ ,T
EXE
then
F6
to draw
Note: You cannot see the line y = 1000x – 2000.
Find the intersection points
(vertices) of the lines that intersect
SHIFT
F5
for G-Solve then
F5
for [ISCT] (intersection)
then select two lines at a time and
generate the 5 intersection points.
Y1 & Y4 gives (2 , 13) Y1 and Y3 gives (3 , 12) Y2 and Y4 gives (2 , 6)
Y2 and Y5 gives (3 , 6) Y3 and Y5 gives (4 , 8)
The V-Window
[SHIFT] [F3]
becomes:
Becomes y
1000x - 2000
cont. on next page
Linear programming with vertical lines: converting x = c to y = mx + c [in GRAPH] cont.
Using the original equations:
y 15 – x y 6 y 24 - 4x x 2 y 2x gives:
Note:
You can see the line x = 2 but G-Solve is not available for the vertical line x = 2.
Some interpretation is required if the substitution line for x = c is not ‘extremely’
vertical on the region the constraints are drawn.
Factorials, Combinations and Permutations – Calculations [in RUN-MAT]
Combinations and Permutations – x!,
n
Cr and
n
Pr respectively
KEY RESULT
MISCELLANEOUS FUNCTIONS