Consider the following linear programming problem. A medical doctor works in 2 private clinics: Medicare Clinic and Millennium Clinic. By logistic limitations, she cannot work in both clinics on the same day. This is, she works in one clinic on some days, and in the other clinic on other days. When the doctor works one day at Medicare Clinic, she can provide medical attention to 8 children

Consider the following linear programming problem. A medical doctor works in 2 private clinics: Medicare Clinic and Millennium Clinic. By logistic limitations, she cannot work in both clinics on the same day. This is, she works in one clinic on some days, and in the other clinic on other days. When the doctor works one day at Medicare Clinic, she can provide medical attention to 8 children and 5 adults, and she spends 1.8 hours driving back and forth from her home to that clinic. When the doctor works one day at Millennium Clinic, she can provide medical attention to 4 children and 7 adults, and she spends 1.2 hours driving back and forth from her home to that clinic. This medical doctor has a goal: to provide medical attention to at least 451 children and 401 adults within 80 working days. How many days should the medical doctor work in each clinic so that she achieves her goal while minimizing the total driving time?

a) Define your variables using full sentences.

b) Write the objective (Minimize or Maximize) and the objective function.

c) State the constraints. Do NOT find the feasible set.

d) For this linear programming problem, the corner points of the feasible set and the values of the objective function at these points are given below.

Corner Point: (17,63), (53,27), (32,39)

Value of objective function on cornerpoint: 106.2, 127.8,104.4

The ordered pairs in the table above are in the form (Medicare, Millennium) and the values of the objective function are measured in hours.

How many days should the medical doctor work in each clinic so that she achieves her goal while minimizing the total driving time? What is the minimum total driving time possible?