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Summary Notes for OPTIMIZATION problems from differential calculus (MATH 184, UBC) CA$14.06
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Summary Notes for OPTIMIZATION problems from differential calculus (MATH 184, UBC)
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You will find step-by-step solutions to difficult optimization problems within this document. Work through them and then check your answers to guarantee success in your calculus course.

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  • January 12, 2021
  • 11
  • 2020/2021
  • Summary

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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)

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