Problems for "Optimization"
Problem 9.1:
Find 2 positive numbers whose product is 25 and whose sum is a minimum.
[Solution]
Problem 9.2:
What is the maximum value of
f (x) = x4 -8x2 - 3 on the interval
[- 3, 3]?
[Solution]
Problem 9.3:
A shepherd wishes to build a rectangular fenced area against the side of a barn. He has 360 feet
of fencing material, and only needs to use it on three sides of the enclosure, since the wall
of the barn will provide the last side. What dimensions should the shepherd choose to
maximize the area of the enclosure?
[Solution]
Problem 9.4:
Find the point on the graph of
y = x2 that is the smallest distance from the point
(0, 6).
[Solution]
