Consider the general supply function:

Q_s = 60 + 5P - 12P_I + 10F

where Q_s = quantity supplied, P = price of the commodity, P_I = price of a key input in the production process, and F = number of firms producing the commodity.
a. Interpret the slope parameters on P, P_I, and F.
b. Derive the equation for the supply function when P_I = $90 and F = 20.
c. Sketch a graph of the supply function in part b. At what price does the supply curve intersect the price axis? Give an interpretation of the price intercept of this supply curve.
d. Using the supply function from part b, calculate the quantity supplied when the price of the commodity is $300 and $500.

e. Derive the inverse of the supply function in part b. Using the inverse supply function, calculate the supply price for 680 units of the commodity. Give an interpretation of this supply price.