Consider a competitive firm with the following cubic cost function: C(q) = 0.008q3 -0.08q2 +22q + 8. (a) Derive the following three functions: Average Cost AC(q), Average Variable Cost AV C(q), and Marginal Cost MC(q). (b) Present a table with the following four columns: q, MC(q), AV C(q), and AC(q) for integer values of q between 2 and 12 (this is 11 rows). Include the cost numbers in the table rounded to 3 decimal places. You may want to use a formulas in MSExcel, or other software, to accurately calculate the various costs for different values of q. (c) Sketch a graph of the MC(q), AV C(q), and AC(q) functions. (d) At what quantity is Average Cost at its minimum? (e) Show that the Marginal Cost function equals the Average Cost function at mini- mum Average Cost. Also, show that the slope of AC(q) equals zero (dAC(q)/dq= 0) at its minimum. (f) In the short run, in what price range would the firm decide to shut down and produce zero units? Explain.