Johnson & Johnson (J&J) y is ready to start making Covid-19 vaccines for the world. The cost of producing a single dose of a vaccine is $10. Clearly, the immediate priority of the company is to produce enough vaccines for the vulnerable population of the US to whom the vaccine will be offered for a low price equal to $15 per person. The US population is hesitant about trying out the new vaccine and as a result the company is unsure about whether the vaccine will be well adopted among the vulnerable population. With probability 30% the adoption will be High in which case 30 million people will request a vaccine, with probability 20% the adoption will be Medium in which case 20 million people will request a vaccine, and with probability 50% the adoption will be Low in which case 10 million people will request a vaccine. If a vaccine is not available for the US population the company will need to enable the emergency mode in which case the cost of producing one vaccine goes up to $50. Johnson & Johnson must produce enough vaccines to match the US demand in the case there is a shortage. Finally, J&J can also sell vaccines for $20 each to Europe, however, any vaccines produced for the US cannot be sold in Europe and must be discarded.

a. How many vaccines should J&J produce for the US market?

b. What is the expected Profit from the US market?

c. How many vaccines are expected to be produced and wasted?