Polynomials

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Polynomials

• Word Problems

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Learning Goal

• I will be able to apply my knowledge of
  polynomial functions to real-life problems.

3
Polynomial Word ProblemsOpen Box
An open box can be made by cutting out squares
from the corners of a 9-inch by 12-inch
rectangular sheet of cardboard and folding up the
sides. Find the maximum volume of the box and
the dimensions which yield the maximum volume.
Diagram
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Polynomial Word Problems Open Box
An open box can be made by cutting out squares
from the corners of a 9-inch by 12-inch
rectangular sheet of cardboard and folding up the
sides. Find the maximum volume of the box and
the dimensions which yield the maximum volume.
Function
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Polynomial Word Problems Open Box
An open box can be made by cutting out squares
from the corners of a 9-inch by 12-inch
rectangular sheet of cardboard and folding up the
sides. Find the maximum volume of the box and
the dimensions which yield the maximum volume.
Sketch
D (0, 4.5) rw R (0, 81.872) rw
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Polynomial Word Problems Open Box
An open box can be made by cutting out squares
from the corners of a 9-inch by 12-inch
rectangular sheet of cardboard and folding up the
sides. Find the maximum volume of the box and
the dimensions which yield the maximum volume.
(1.697, 81.872)
Solution Maximum
Maximum Volume 81.872 cubic inches
Dimensions 1.697 inches by 5.606 inches by 8.606
inches
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Polynomial Word ProblemsThe package
A package may be sent by mail only if the sum of
its height and the perimeter of the base is not
more than 72 inches. Find the dimensions of the
box of maximum volume that can be sent if the
base of the box is a square.
Diagram
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Polynomial Word ProblemsThe package
A package may be sent by mail only if the sum of
its height and the perimeter of the base is not
more than 72 inches. Find the dimensions of the
box of maximum volume that can be sent if the
base of the box is a square.
Function
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Polynomial Word ProblemsThe Package
A package may be sent by mail only if the sum of
its height and the perimeter of the base is not
more than 72 inches. Find the dimensions of the
box of maximum volume that can be sent if the
base of the box is a square.
Sketch
D (0, 18) rw R (0, 3456) rw
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Polynomial Word ProblemsThe Package
A package may be sent by mail only if the sum of
its height and the perimeter of the base is not
more than 72 inches. Find the dimensions of the
box of maximum volume that can be sent if the
base of the box is a square.
(12, 3456)
Solution Maximum
Maximum Volume 3456 cubic inches
Dimensions 12 inches by 12 inches by 24 inches
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Polynomial Word ProblemsThe Box with Lid
Two congruent squares are removed from one end of
a rectangular 10-inch by 20-inch piece of
cardboard. Two congruent rectangles are removed
from the other end as shown. Determine the value
of x so that the resulting box has maximum
volume. What is the maximum volume?
Diagram
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Polynomial Word ProblemsThe Box with Lid
Two congruent squares are removed from one end of
a rectangular 10-inch by 20-inch piece of
cardboard. Two congruent rectangles are removed
from the other end as shown. Determine the value
of x so that the resulting box has maximum
volume. What is the maximum volume?
Function
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Polynomial Word ProblemsThe Box with Lid
Two congruent squares are removed from one end of
a rectangular 10-inch by 20-inch piece of
cardboard. Two congruent rectangles are removed
from the other end as shown. Determine the value
of x so that the resulting box has maximum
volume. What is the maximum volume?
Sketch
D (0, 5) rw R (0, 96.225) rw
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Polynomial Word ProblemsThe Box with Lid
Two congruent squares are removed from one end of
a rectangular 10-inch by 20-inch piece of
cardboard. Two congruent rectangles are removed
from the other end as shown. Determine the value
of x so that the resulting box has maximum
volume. What is the maximum volume?
(2.113, 96.225)
Solution Maximum
Maximum Volume 96.225 cubic inches
Dimensions 2.113 inches by 7.887 inches by 5.774
inches
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Learning Goal

• I will be able to apply my knowledge of
  polynomial functions to real-life problems.

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End of notes.

• Now do Polynomial Word Problem Assignment.