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 “emergency mode” 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.

  1. a) How many vaccines should Jones&Jones produce for the US market?


  2. b) What is the expected profit?


  3. c) How many vaccines are expected to be produced and wasted (expected value)?

    5 million

Please help me by showing work to these questions, Thank you

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