The following general supply function shows the quantity of good X that producers offer for sale (Q_s):

Q_s = 19 + 20P_s - 10P_I  + 6T - 32P_r - 20P_e + 5F

where P_x is the price of X, P_I is the price of labor, T is an index measuring the level of technology, P_r is the price of a good R that is related in production, P_e is the expected future price of good X, and F is the number of firms in the industry.
 a. Determine the equation of the supply curve for X when P_I = 8, T = 4, P_r = 4, P_e = 5, and F = 47. Plot this supply curve on a graph.
 b. Suppose the price of labor increases from 8 to 9. Find the equation of the new supply curve. Plot the new supply curve on a graph.
 c. Is the good related in production a complement or a substitute in production? Explain.
 d. What is the correct way to interpret each of the coefficients in the general supply function given above?