Download (38) 4.7 Optimization Problems(B) - eng

(38) 4.7
Example 1
28 Dec 20,
2001
Optimization Problems(B)
(4 pts.) A closed box with a square base is to be made to have a volume of
. If the cost of the material used is 50 cents per
and if there is
no waste of material . Find the dimensions that will minimize the cost of
the material .
Solution
y
x
x
Example 2
26 May 10,
2001
A box of a rectangular base and an open top has surface area of
.
If the height of the box is equal to its width , find the dimensions that give
the box a maximum volume .
Solution
y
y
x
(38) 4.7 Optimization Problems (B)
Example 3
P2
A rectangular storage container with an open top is to have a volume of
. The length of its base is twice the width. Material for the base costs
$ per square meter. Material for the sides costs $ per square meter.
Find the cost of materials for the cheapest such container.
Solution
y
x
HOSSAM GHANEM
86881166
‫حسام غانم‬
(38) 4.7 Optimization Problems (B)
Example 4
P3
What is the maximum vertical distance between the line
and the parabola
for
Solution
Example 5
What is the minimum vertical distance between the parabolas
and
Solution
HOSSAM GHANEM
86881166
‫حسام غانم‬
(38) 4.7 Optimization Problems (B)
Example 6
P4
Find the point on the line
that closest to the origin
Solution
At
the point
HOSSAM GHANEM
86881166
‫حسام غانم‬
(38) 4.7 Optimization Problems (B)
P5
Homework
1
17 January 8 ,1997
Find the dimensions of the rectangle of maximum area whose perimeter is 100 ft.
2
30 Jan. 12. 2008
Find the maximum area of the rectangle that can be inscribed inside a semi-circle of radius 2
3
31 June 5, 2008
A farmer has 200 meters of fence to be used in constructing three sides of a rectangle.
An existing long straight wall is to be used for the fourth side. What dimension will
maximize the area of the rectangle?
4
18 May 24 ,2000
Find the dimensions of the rectangle of maximum area whose diagonal is 2ft..
5
31 July 31st , 2003
Let x and y be two real numbers where:
Find x and y such that
is minimum
6
9 January 8, 1994
A wire 17 cm long is cut into two pieces. On piece is bent into the shape of a square and the
other into the shape of a rectangle whose length is twice its width. .Where should the wire be
cut so that the sum of areas of the square and rectangle is minimum?
.
57 April 27 , 2013
7
8
Find two of positive numbers whose product is
and whose sum is a minimum
43 July 29, 2012
5. (3 Points )
Find two nonnegative numbers whose sum is 100 and their product is maximum.
HOSSAM GHANEM
86881166
‫حسام غانم‬
(38) 4.7 Optimization Problems (B)
6
9 January 8,
1994
P6
A wire 17 cm long is cut into two pieces. On piece is bent into the shape of
a square and the other into the shape of a rectangle whose length is twice
its width. .Where should the wire be cut so that the sum of areas of the
square and rectangle is minimum?
Solution
6y
4x
y
x
2y
x
the wire should be cut into two pieces its longs
HOSSAM GHANEM
86881166
‫حسام غانم‬