It is assumed that the total cost in dollars of manufacturing q units of a certain item is given by the function C(q)=-x^3-30q^2+400q+500 a) Calculate the cost of manufacturing 20 units. b) Calculate the cost of manufacturing the twentieth unit. Suppose the number of worker-hours needed to distribute the new telephone directories to x% of households in a certain rural community is given by the function f(x)=600x/300-x a) What is the domain of the function? b) In this context, for what values of x does f(x) a practical interpretation? c) How many worker-hours were needed to distribute the new telephone directories to the first 50% of dwellings? d) How many worker-hours were needed to distribute the telephone directories to the entire community? e) What percentage of dwellings in the community did you receive the new phone directories after 150 worker-hours? In a factory, the total cost of crafting q units during one day of work is C(q) = q^2+ q + $900. In a typical work day, during the first t hours they make q(t) = 25t units. a) Express the total manufacturing cost as a function of t. b) How much will have been spent on production at the end of the third hour? c) When will the total manufacturing cost reach the $11,000?