A manufacturer determines that the supply function for x units of a particular commodity is S(x) = ln(x + 2) and the corresponding demand function is D(x) = 10 − ln(x + 1).

a. Find the demand price p = D(x) when the level of production is x = 10 units.

b. Find the supply price p = S(x) when x = 100 units.

c. Find the level of production and unit price that correspond to market equilibrium (where supply = demand).