A new life-saving vaccine is now available on the market. The CEO of FastMed, which operates a nationwide chain of 1,100 locations, is deciding whether the vaccine should be made available via its locations. With the state of the pandemic, they anticipate having more demand than they can serve.

All locations are exactly identical to each other. Each location has seven exam rooms, one receptionist, four doctors, and three nurses on staff 8 hours a day.

Currently, each patient's visit takes 2 minutes of the receptionist's time, 5 minutes of a nurse's time, and 15 minutes of a doctor's time.

A vaccine visit would take 2 minutes of the receptionist's time, 5 minutes of a nurse's time, plus 15 minutes of observation.

The nurse's and doctor's part of the visit happens in the exam room, while the receptionist's part of the visit and observation happens in the reception area. The exam room could have only one patient at a time, and the reception area has five chairs (i.e., it could hold five socially-distant patients under observation).

Assume all patients could be scheduled (and do arrive) so that they don't have to wait in the reception for any other reason than the observation after the vaccine (check-in with the receptionist does not require a chair).

The marginal contribution of a doctor's visit is $100, and of vaccination visit is $50.

a. [5] How many vaccine visits should each location offer? How much extra money would this bring? Would offering vaccine visits compromise the care of regular patients (i.e., will FastMed choose to have fewer doctor visits in favor of vaccination visits)?

While doctors and nurses are in short supply, each location could hire another receptionist and/or buy an extra chair.

b. [2]Would you recommend hiring an additional receptionist and/or buying an extra chair? What would be the highest amount you are willing to pay for the addition(s) that you recommend?