Find the dimension of the box that will minimize the total cost. Find the minimum total cost ?
1 Answer
base length=height=
cost
Explanation:
consider the block with square base of side length
for minimum cost it must have minimum surface area
however the volume is fixed
we have volume
we have surface area as function of side
(this involves two variables(
substituting for
or
for any function to be minimum or maximum its first derivative must be 0
we have
for minimum surface area(or maximum)
to check if it is point of maxima or minima we have second derivative test
we have
put
if it is positive it is point of minima if it is negative it is point of maxima(if it is 0 it is point of inflexion)
here
hence
area of bases=
area of sides=
minimum cost=
by the way what currency is "Birr" : )