# 3.7 PP

```Miss Battaglia
AB/BC Calculus
We need to enclose a field with a fence. We have
500 feet of fencing material and a building is on one
side of the field and so won’t need any
fencing. Determine the dimensions of the field that
will enclose the largest area.
1.
2.
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4.
5.
Identify all given quantities and all quantities to be
determined. If possible, make a sketch.
Write a primary equation for the quantity that is to be
maximized or minimized.
Reduce the primary equation to one having a single
independent variable. This may involve the use of
secondary equations relating the independent
variables of the primary equation.
Determine the feasible domain of the primary
equation. That is, determine the values for which the
stated problem makes sense.
Determine the desired maximum or minimum value
by the calc techniques we learned this chapter.
A manufacturer wants to design an open box
having a square base and a surface area of 108
square inches. What dimensions will produce a
box with maximum volume?
h
x
x
We want to construct a box whose base length is 3
times the base width. The material used to build the
top and bottom cost \$10/ft2 and the material used
to build the sides cost \$6/ft2. If the box must have
a volume of 50ft3 determine the dimensions that will
minimize the cost to build the box.
Two posts, one 12 feet high and the other 28 feet
high, stand 30 feet apart. They are to be stayed by
two wires, attached to a single stake, running from
ground level to the top of each post. Where should
the stake be placed to use the least amount of wire?