AbbVie Pharmaceuticals $($headquartered in Lake Forest, IL$)$ has commenced a $$10$ million R&D project to develop a new drug to treat a rare disease. So far, it has spent $$6$ million of the $$10$ million, and preliminary results are positive. If the additional $$4$ million is invested, the drug will certainly be completed and is expected to generate profit of $$18$ million in present value for AbbVie. Meanwhile, a research biologist at Illinois Tech has independently developed a treatment for the same disease. The scientist has offered to sell her invention to AbbVie. Her drug would be just as effective as AbbVie$$s drug, and would also generate profit of $$18$ million in present value. Refer to the above text. Suppose that Merck has also expressed interest in the biologist$$s invention. If Merck buys the drug, there is a $50\%$ chance that it will beat AbbVie$$s drug to market. If that happens, suppose the profit of the second drug to market is zero. Now how much should AbbVie be willing to pay for the drug? How much should Merck be willing to pay?

a$)$ $$18$ million for AbbVie and $$9$ million for Merck.

b$)$ $$4$ million for AbbVie and $$18$ million for Merck

c$)$ $$9$ million for AbbVie and $$9$ million for Merck.

d$)$ $$13$ million for AbbVie and $$9$ million for Merck.