A 1 litre glass cylindrical mug having a pewter lid is constructed.

a) Show that if glass costs 10 cents per cm^2 and pewter costs 20 cents per cm^2, then the total cost (C) for materials (in dollars) is given by

C(x) =((3*pi*(x^2))/40)+(400/x);

where x is the diameter of the mug in cm. Recall that 1 litre = 1,000 cm^3.

b) Find the dimensions (diameter and height) which minimizes the cost.