Page 24 - Math SL HB Sem 2

OPTI]VIISATION

Many problems where we try to find the maximum or minimum value of a variable
can be solved using differential calculus techniques. The solution is often referred
to as the optimum solution.

Example l:

An open+op box is to be made from a square of sheet metal 40cm on a side by
cutting a square from each comer and bending up the sides along the dashed line in
Figure l. Find the dimension xofthe cutout that will result in aboxof the greatest
volume.
I

oc.^
I I
t

*o Lr.

Example 2:
Find the most economical shape (minimum open
Surface area) for a box with a square base,
.rertical sides and an open top, given that it
must contain 4 liters.