The Modema vaccine has just passed Phase 3 of testing and the company is ready to start producing 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. Modema must produce enough vaccines to match the US demand in the case there is a shortage. Finally, Modema 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 Modema produce for the US market?

b. Based on your answer in part a), what is the expected Profit from the US market?

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