his is Section 3.8 Problem 22:A firm receives an order for a square-base rectangular storage container with a lid. The container has a volume of 20 cubic meters. Material for the base costs 20 dollar per square meter. Material for the sides and the lid costs 10 dollars per square meter. What is the lowest cost of materials for making such a container? What are the dimensions of the container that require the lowest cost for materials? Follow the steps:(a) Let the length of the base to be x and the height to be h. Then the quantity to be minimized is (expressed as a function of both x and h) C= .(Use fraction for coefficients.)(b) The condition that x and h must satisfy is h= .(c) Using the condition to replace h by x in C, C can then be expressed as a function of x: C(x)= .(d) The domain of C is (,).(Use ``infty'' for .)(e) The only critical number of C in the domain is x= .(Keep 2 decimal place (rounded)). We use the Second-Derivative Test to classify the critical number as a relative maximum or minimum, or neither: