Page 1 | © 2012 by Janice L. Epstein 5.5 □ Applied Max and Min problems Applied Maximum and Minimum Problems
(Section 5.5)
Page 2 | © 2012 by Janice L. Epstein 5.5 □ Applied Max and Min problems EXAMPLE 3
Find the point on the line y = 2 x - 3 that is the closest to (-1,3).
EXAMPLE 1
A company wishes to design a rectangular box with a square base
and no top. The volume of the box is 27 cubic inches. The cost
per square inch of the bottom is twice the cost of the sides. What
are the dimensions of the box that has the minimum cost?
3
2
1
-1
1
2
3
-1
-2
-3
EXAMPLE 2
A poster is to have an area of 180 in2 with 1 in margins on the
sides and bottom and 2 in margin on the top. What dimensions
will give the largest printed area?
EXAMPLE 4
Find the dimensions of the rectangle of the largest area that has its
base on the x-axis and the other two vertices above the x-axis lying
on the parabola y = 8 - x 2
9
8
7
6
5
4
3
2
1
-3
-2
-1
1
2
3
Page 3 | © 2012 by Janice L. Epstein 5.5 □ Applied Max and Min problems EXAMPLE 5
Pipe needs to be laid connecting A with B. The cost along the
level stretch A to C is $10 per foot. The cost along the diagonal
stretch from C to B is $30 per foot. At what point C will the cost
of laying the pipe be minimized?
B
30’
D
C
40’
A
Page 4 | © 2012 by Janice L. Epstein 5.5 □ Applied Max and Min problems EXAMPLE 6
A piece of wire 10 m long is cut into two pieces. One piece is bent
into a circle and the other piece is bent into a square. How should
the wire be cut so that the total area enclosed is minimized? How
should the wire be cut to maximize the total area enclosed?