The Jones&Jones 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 â€œemergency modeâ€ in which case the cost of producing one vaccine goes up to $30. Jones&Jones must produce enough vaccines to match the US demand in the case there is a shortage. Any unused vaccines cannot be sold and must be discarded.
a) How many vaccines should Jones&Jones produce for the US market?
b) What is the expected profit?
c) How many vaccines are expected to be produced and wasted (expected value)?
Please help me by showing work to these questions, Thank you