Download Max-Min Worksheet #1

Page 1 Part 1
1. A closed top box with a square base has a volume of 800 m2 . Find the dimensions of the box that will
minimize the materials used.
2. If farmer Joe has to build 3 rectangular pastures of the same size for his cow, his horse, and his pig and he
only has 192m of fence. Find the dimensions of his pastures so that the area is the largest possible.
3. Find the points on the curve y= 6 - x2 that are nearest the point (0,3).
4. Two numbers add up to 36. Find these numbers so that the product is a minimum.
5. An oil can has a capacity of 3L. Find the dimensions of the can so that the least materials possible are used.
6. An oil can has a capacity of 1L. If the ends are 7$ each and the sides are 4$ each, find the dimensions so that
1. Find
two numbers
add up to give you 48 and whose product is a maximum.
the
construction
costswhich
are minimized.
7. Two numbers add to give you 28. Find these numbers so that the quotient is a minimum.
8.
cone
shaped
water
tankadd
hasup
a volume
the dimensions
tank that will minimize materials
1. A
Find
two
numbers
which
to give of
you1L.
48 Find
and whose
product isofa the
maximum.
needed.
2. Two numbers have a difference of 40. Find the two numbers whose product is a
9. Using 4x+y=16, find the values of x and y so that its product yields a maximum.
minimum.
1. Find two numbers which add up to give you 48 and whose product is a maximum.
2
10. An open toped box that has a square base also has a volume of 2000 cm . If the base is 3$ and the sides are
2$
each, findnumbers
the dimensionsadd
thatupwill
minimize
theand
construction
costs. a maximum.
1.
to 40.
give
youthe
48
product
2. Find
Two two
numbers havewhich
a difference
of
Find
two whose
numbers
whoseisproduct
is a
3. Find two numbers whose product is 100 such that the sum of one number and twice
minimum.
Part
2
the second number is a maximum.
1. Find two numbers which add up to give you 48 and whose product is a maximum.
2. Two numbers have a difference of 40. Find the two numbers whose product is a
3. Find two numbers whose product is 100 such that the sum of one number and twice
minimum.
2.
numbers
have
difference of 40. Find the two numbers whose product is a
theTwo
second
number
is aa maximum.
minimum.
4. An oil can has a holding capacity of 1 litre. What are the dimensions of the can which
3.
Find twothe
numbers
product
100 such that the sum of one number and twice
minimizes
costhave
ofwhose
materials
. ofis40.
2. Two numbers
a difference
Find the two numbers whose product is a
the second number is a maximum.
3.minimum.
Find two numbers whose product is 100 such that the sum of one number and twice
theAn
second
number
is a maximum.
4.
oil can
has a holding
capacity of 1 litre. What are the dimensions of the can which
minimizes the cost of materials.
3. Find two numbers whose product is 100 such that the sum of one number and twice
5.the
A second
container
in theisshape
of a cylinder with an open top has a capactiy of 24 cm 2 .
number
a maximum.
4. An oil can has a holding capacity of 1 litre. What are the dimensions of the can which
What are the dimensions that will minimize the cost of production if the box bottom is
minimizes the3 cost of materials.
2
4. An oil
holding
of 1 litre.
of the can which
$6.00
percan
cm has
andathe
sides ocapacity
f the container
areWhat
$2.00are
perthe
cmdimensions
.
minimizes the cost of materials.
5. A container in the shape of a cylinder with an open top has a capactiy of 24 cm 2 .
What are the dimensions that will minimize the cost of production if the box bottom is
4. An oil can has a holding capacity of 1 litre. What are the dimensions of the can which
$6.00 per cm3and the sides of the container are $2.00 per cm 2 .
minimizes the cost of materials.
5. A container in the shape of a cylinder with an open top has a capactiy of 24 cm 2 .
What are the dimensions that will minimize the cost of production if the box bottom is
5. A container in the shape of a cylinder with an open top has a capactiy of 24 cm 2 .
7. Find the dimensions of a box with a square base and an open top with 3a maximum
6. A box that has a square base and an open top has a volume of 8000cm . Find the
2
volume
that wants
can beto
built
for
Thecost
material
forAfter
the base
costs
and the
material
8.
A farmer
fence
in$2400.
his rectangular
fencing
the$8/m
perimeter
he wants
to
dimensions
which
would
minimize
the
offield.
materials.
Page 2
2
for the sides
.
subdivide
thecosts
field$4/m
into three
smaller rectangular sections. Unfortunantely the farmer can only
3a maximum
7.
Find
the
dimensions
of abase
box
withana open
square
base
an open
op
with
afford
100
meters
fencing.
Determine
the top
possible
that
would
maximize
the area.
6. A
box
that
has aofsquare
and
hasand
a dimensions
volume
of t8000cm
. Find
the
8. A farmer wants to fence in his rectangular field. After fencing the perimeter
he wants to
2
volume that which
can bewould
built for
$2400. the
Thecost
material
for the base costs $8/m and the material
dimensions
minimize
of materials.
subdivide the field into three
smaller
rectangular
sections.
Unfortunantely the farmer can only
for the sides costs $4/m 2 .
afford 100 meters of fencing. Determine the possible dimensions that would maximize the area.
7. Find the dimensions of a box with a square base and an open top with a maximum
2
8.
A farmer
fence
his rectangular
field.forAfter
fencing
the$8/m
perimeter
he wants
to
volume
that wants
can betobuilt
forin$2400.
The material
the base
costs
and the
material
subdivide
the field into three
smaller rectangular sections. Unfortunantely the farmer can only
9.
forThe
the Canadian
sides costsWildlife
$4/m 2 . Company wants to preserve a section of precious land. One side of the
afford
fencing.
Determine
the possible
dimensions
that
would
maximize
rectangular
plot is of
against
lake.
If you
don't
include
this
will
maximi
zedthe area.
7.
Find100
the meters
dimensions
of aa box
with
a square
base and
anside,
openwhat
top
with
athe
maximum
dimensions
of the remaining
sides
be if they can't
total
more
thanthe
36km?
2
8.
A farmer
fence
his rectangular
field.for
After
fencing
perimeter
he wants
to
volume
that wants
can betobuilt
forin$2400.
The material
the base
costs $8/m
and the
material
9. The Canadian Wildlife Company wants to preserve a section of precious land. One side of the
2
subdivide
thecosts
field into three
smaller rectangular sections. Unfortunantely the farmer can only
for
the sides
rectangular
plot is $4/m
against. a lake. If you don't include this side, what will the maximized
afford 100 meters of fencing. Determine the possible dimensions that would maximize the area.
dimensions of the remaining sides be if they can't total more than 36km?
8. A farmer wants to fence in his rectangular field. After fencing the perimeter he wants to
9. The Canadian Wildlife Company wants to preserve a section of precious land. One side of the
subdivide the field into three smaller rectangular sections. Unfortunantely the farmer can only
rectangular
plot
is against
a lake. If yyou
include
this side,
will (0,3).
the maximized
10.
Find
themeters
points
the parabola
 6don't
the
x 2 possible
that
are dimensions
closest
to what
thethat
point
afford
100
ofonfencing.
Determine
would maximize the area.
dimensions of the remaining sides be if they can't total more than 36km?
8. A farmer wants to fence in his rectangular field. After fencing the perimeter he wants to
9.
The Canadian
Wildlife
Company
wants to2 preserve
a section
of preciousthe
land.
Onecan
sideonly
of the
subdivide
thepoints
field
into
three
smaller
Unfortunantely
farmer
10.
Find the
on the
parabola
y rectangular
6  x thatsections.
are closest
to the point (0,3).
rectangular
plot is of
against
a lake.
If you don't
include dimensions
this side, what
the maximi
zedthe area.
afford
100 meters
fencing.
Determine
the possible
thatwill
would
maximize
dimensions of the remaining sides be if they can't total more than 36km?
11.
FindCanadian
the point(s)
on theCompany
line y  5wants
x  4 that
is closest
to the origin.
9. The
Wildlife
to preserve
a section
of precious land. One side of the
10.
Find theplot
points
on the parabola
 6don't
 x 2 that
are closest
to what
the point
rectangular
is against
a lake. If yyou
include
this side,
will (0,3).
the maximized
dimensions of the remaining sides be if they can't total more than 36km?
11. Find the point(s) on the line y  5 x  4 that is closest to the origin.
9. The Canadian Wildlife Company wants to preserve a section of precious land. One side of the
10.
Find theplot
points
on the parabola
 6don't
 x 2 that
are closest
to what
the point
rectangular
is against
a lake. If yyou
include
this side,
will (0,3).
the maximized
dimensions of the remaining sides be if they can't total more than 36km?
11. Find the point(s) on the line y  5 x  4 that is closest to the origin.
10. Find the points on the parabola y  6  x 2 that are closest to the point (0,3).
11. Find the point(s) on the line y  5 x  4 that is closest to the origin.
10. Find the points on the parabola y  6  x 2 that are closest to the point (0,3).
11. Find the point(s) on the line y  5 x  4 that is closest to the origin.
11. Find the point(s) on the line y  5 x  4 that is closest to the origin.