As the staff director of a new hospital you are planning to

As the staff director of a new hospital, you are planning to hire cardiologists, rehabilitation specialists, and infectious disease specialists. According to recent data, each cardiology case averages $12,000 in revenue, each physical rehabilitation case$19,000 and each infectious disease case, $14,000. You judge that each specialist you employ will expand the hospital caseload by about 10 patients per week. You already have 3 cardiologists on staff, and the hospital is equipped to admit up to 200 patients per week. Based on past experience, each cardiologist and rehabilitation specialist brings in one government research grant per year, while each infectious disease specialist brings in three. Your board of directors would like to see a total of at least 30 grants per year and would like your weekly revenue to be as large as possible.  

How many of each kind of specialist should you hire?

a. State the LP in standard form, defining all variables.

b. Solve the LP with the online solver and attach a printout of the solution at the end of the project. In complete sentences, state your solution to the problem. How many of each kind of specialist should you hire?

Solution

So we must have C+P+I <= 197

  c+p+3i >=27

Subtract to get 2i = 170 or i = 85

c+p<= 112

i.e. 9<i<197

27<c<197

27<p<197

Since revenue is maximum for P and minimum for c, only minimum number of c can be taken.

Hence ideal solution would be

c=0, p =197, i = 0

so that revenue = 197(19000) = 3743000

and grant would be 197 greater than 30