Suppose a company has the following cost function:

C(q) = 5000 + 100q + 2q^2

where q is the quantity produced.

a) Find the total cost of producing 100 units of output.
b) Calculate the average variable cost (AVC) and average total cost (ATC) at a quantity of 100 units.
c) Find the marginal cost (MC) function for this cost function.
d) Determine the quantity of output that minimizes average total cost (ATC).