Summary STK120 - Linear programming notes

, Lecture 1




What mathematical technique function
is
modelling
I
linear
programming ? in which linear is to be
a a


maximized or minimized when
subjected to various constraints

optimized restrictions



Example ;
·
Aircraft A = x
Y 1) 3
2) ~
mu
·
Aircraft B =

Y T The objectivistominimizea
in the objective function
function
objective 200x
240y
+
- : minimize


i
3)
- P
Complete table :


per flight
- Constraints Aircraft A(x) Aircraft B(y) Restrictions
1
-
smallest 1)
100 60 > 1200
Passengers
2)
2)
2000 3000 336000
constraints
Luggage
:.
; 3)
I I - 16

G0y) Flights
(
+




C
1 100x , 1200 ava




don't know
22000x +
3000y36000 we exactly how
many flights
Per aircraft , so we put Is

3x + -16
y of
always whole purpose is to find these values
will

yo be a restriction
&y that will minimize costs




To Plot Constraints dual method




·
-P Use int

sub 0 for X solve for y
y-int x-int ,



1 (0 ; 20) ,
(12 ; 0) ·
subo for
y ,
solve for x




2 10 ; 12) (18 ; 0)
,




3(16 ; 0) (0 ; 16)
,
O
. is is




Find feasible
Region sub in 10 for ec in
every constraint
.
,
y
·
see if it satisfies inequality

find where all constraints are satisfied
region


&
-
The are
pi
will minimize costs ?
points method
which one
method
,
Graphical 2 Extreme
There are 2 methods ;

1) function A(8 6 64)
y objective
solve will be
S in ↳
given
.




...
-
,

I
B(6 ; 10)
20y -2000 -40
=
-




248 c(12 ; 4)
1 . 1 1 i
b .2
&
is is
y
-
=
-x +
=240 ↓
L 1) sub each ec and
Y
into
/
function
objective
: Point A will minimize costs
,
what are the co-ordinates ? 2) Plot gradient e



dotted upward ,

&
If line
Point A O and & intersect , we move
2) that smallest
At ,
line one
gives an

of A
find intersection to
get
co-ordinate touches point A first is
point A