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Max-Min Problems Quiz 1.0 EF
1. Let A equal the area of a rectangle with fixed perimeter, P. Show that the largest value
p2
of A is
. (OR try an easier version with P = 12 m)
16
2. A cardboard box of 32 m3 volume with a square base and open top is to be constructed.
Find the minimum area of cardboard needed. (Neglect wasted cardboard.)
3. The Acme Company’s daily profit is given by the following equation:
P( x)  .03x3  36 x  500 for x  0 where x is the number of 'widgets' sold each day.
Maximize Acme’s daily profit.
4. A right circular cone is inscribed in a hemisphere of radius 2m. Find the dimensions
(h and r) of the cone of maximum volume. (a) cone base resting on the curved surface
of the inverted hemisphere on the right with the tip of the cone no higher than the
circle.
5. Find two postive numbers whose sum is 8 such that when the cube of the first number
is multiplied by the second number, the result in a maximum.