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| PAGE: 213 | SET: Exercises | PROBLEM: 54 |
(a).
Volume of the closed box with a square base is 
cub. in
The volume 
and square area 
of a box with square base length 
and height 
.
Therefore, 
.
(b).
(1). Draw the coordinate plane.
(2). Graph the function .
Graph :
.
(c).
The minimum amount of cardboard used corresponds to the graph of 
with the smallest
-coordinate.
Graph :
Observe the garph :
The graph has minimum point at 
.
Therefore, the minimum amount of cardboard used is 
and this occurs when 
.
(d).
Consider .
Differentiate the above function with respect to .
Equate 
to zero.
The dimensions of the box that minimize the surface area are 
.
(e).
UPS is interested in designing a box that minimizes the surface area because to minimize the cost of materials used for the construction.
(a).
.
(b).
Graph of :
(c).
Minimum amount of cardboard used is and this occurs when .
(d).
.
(e).
To minimize the cost of materials used for the construction.
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