OPTIMIZATION
Find two positive numbers whose product is 81 and whose sum is a
minimum
5- Xty
P= X. y
g= Xt =
X -118111×7
81 = X.
y 81C IX Y
'
s =L
-
+
-
g,
¥ 8¥ cmTY.my
'
S 1
y I
=o
ya
= - -
=
= -
X 2=81
X = I 9
:y= -84=9
a
X =
9
y=9
Find the dimensions of a rectangle with a perimeter of 200 feet with an
area as large as possible
L
P= 2L t
2W A = Lxw
W W
200=2 Lt 2W A =
( 100 W) W -
L
100 =
Lt W A' =
C- 1) CW ) t 400 WII)
-
A
'
= -
2W + 100=0
L =
100 -
W -
2W =
-100
W = 50
1=100 -
SO
L =
SO
, Find the point on the line Y = 4- X that is closest to the point (7,6)
Gib )
¥1
pix "j, pit 6T
'
•
)
,
)
,
- 4 ""
b
q•€f
D= Nz xD
'
Cy
+
g. 5
-
-
.
9=4 X
-
D= a
- .
-
x, +
cap
-
7
4- xD
'
6
-
D= -
X) + -
=(7-X)2-C2t
""
D
'
= I -
X)
'
+ (2-1×5) .
1217 -
X) . -
I + 2C2tx ) ]
4×-10
= = O
2 #
(7 X) t (2-1×5
-
-
x -
1%, y=4
x
-
y -_ 4- ¥=z
Pf 'T ,
E)
Find two positive numbers whose product is 81 and whose sum is a
minimum
5- Xty
P= X. y
g= Xt =
X -118111×7
81 = X.
y 81C IX Y
'
s =L
-
+
-
g,
¥ 8¥ cmTY.my
'
S 1
y I
=o
ya
= - -
=
= -
X 2=81
X = I 9
:y= -84=9
a
X =
9
y=9
Find the dimensions of a rectangle with a perimeter of 200 feet with an
area as large as possible
L
P= 2L t
2W A = Lxw
W W
200=2 Lt 2W A =
( 100 W) W -
L
100 =
Lt W A' =
C- 1) CW ) t 400 WII)
-
A
'
= -
2W + 100=0
L =
100 -
W -
2W =
-100
W = 50
1=100 -
SO
L =
SO
, Find the point on the line Y = 4- X that is closest to the point (7,6)
Gib )
¥1
pix "j, pit 6T
'
•
)
,
)
,
- 4 ""
b
q•€f
D= Nz xD
'
Cy
+
g. 5
-
-
.
9=4 X
-
D= a
- .
-
x, +
cap
-
7
4- xD
'
6
-
D= -
X) + -
=(7-X)2-C2t
""
D
'
= I -
X)
'
+ (2-1×5) .
1217 -
X) . -
I + 2C2tx ) ]
4×-10
= = O
2 #
(7 X) t (2-1×5
-
-
x -
1%, y=4
x
-
y -_ 4- ¥=z
Pf 'T ,
E)
