Let the Demand and Supply for Two Linked Products, Say

Let the demand and supply for two linked products, say corn and soy, be the following: Q_c^d= 12 - 2p_c + p_s; Q_c^s = 4+p_c; Q_s^d = 6-4p_s + p_c; Q_s^s = 4 + p_s. The superscript refers to "demand" (d) or "supply" (s) and the subscript refers to corn (c) or soy (s) . Now, suppose that the demand for corn shifts to Q_c^d = 18 - 2p_c + p_s. If the price of soy does not adjust in response to this shift, what is the new equilibrium price of corn?

A) p_c = 2
B) p_c = 1
C) p_c = 3
D) p_c = 5