Chapter 4.4, Problem 29E

Hint: In exercises 29 and 30, it the coordinates of a boundary point contain fractions, it is wise to obtain the point of intersection algebraically rather than graphically.

Hospital Staffing Levels The equation that represents the proper level of medical staffing in the cardiac care unit of a local hospital is $N\le 2D$, where N is the number of nurses on duty and D is the number of doctors on duty. In order to control costs, the equation $4N+3D\ge 20$ is appropriate. The number of doctors and nurses on duty at any time cannot be negative, so $N\le 0$ and $D\ge 0$.

a. Graph the region satisfying all of the medical requirements for the cardiac care unit. Use the following special graph grid, where D is measured on the horizontal axis and N is measured on the vertical axis.

b. If there are three doctors and two nurses on duty in the cardiac care unit, are all of the medical requirements satisfied?

c. If there is one doctor and four nurses on duty in the cardiac care unit, are all of the medical requirements satisfied?