Optimization 5

Quiz - Optimization 2012.doc
1) A dog breeder wants to install a kennel alongside a building with five equal sized dog
pens. No fence is needed along the building. The fencing used to divide the pens costs $10
per foot, and the fencing used for the exterior of the pens costs $30 per foot. If the dog
breeder wants to spend exactly $1500 on fencing, find the dimensions of the kennel that
will maximize the area.
2) A student wants to find the maximum volume of a box. An equation was determined
and then its derivative was found. Complete the problem and find the value of x that will
maximize the volume. (For full credit, you must show all your work and confirm that you
have found a maximum.)
Derivative equation:
V '  3x 2  19 x  6
3) You have 360 square feet of material to build a rectangular tank with a closed top. The
tank needs to be constructed with a width of 4 meters. Write an equation in terms of x to
find the dimensions of the container which will maximize the volume. The equation must
be simplified and in terms of 1 variable.
Equation to find maximum volume: V=__________________________________
4) The equation given represents the cost of building the cylindrical container below.
Complete the problem by determining the value of ‘r’ which will minimize the cost of
constructing this container. (Round to 4 decimal places.)
 500 
C  4 r  2 r 2 
Cost equation:
 r 
---------------------------------------- Extra credit -------------------------------------------------Use the graph of f’(x) shown to determine at which x-values the original function f(x)
Critical point(s) at x = ______________
Relative maximum(s) at x = ______________
Relative minimum(s) at x = ______________
Graph of f’(x)