An industry is to construct a cylindrical container of fixed volume
V, which is open at the top of. Find the quotient of the height by
radius of the base of the container so that manufacturing cost can be minimal, given that the unit area of the base costs (b) twice the unit area
the lateral surface (a) .
V = π r^2 h
A = π r^2
S = 2πrh (lateral surface)
The Attempt at a Solution
The cost of manufacturing the container is C= C_s + C_a = Α * a + S * b, where b=2a so
C= 2a A + a S = 2πr^2 a + 2πrh a . I understand that we need to form the ratio h/r and regard that as the variable for the cost equation, but I see no way to do so... We are also give that V=constant, but other than the equation r^2 h = Constant I have no clue.