You are in charge of hiring for a major teaching hospital. The hospital has recently expanded the

number of beds available in the Intensive Care Unit (ICU) from 12 to 20. The hospital currently assigns

3 teaching doctors and 8 residents to the ICU, for each of three shifts per day. Due to their experience

teaching doctors can oversee up to 2 patients per shift while residents are only able to treat one.

Experienced doctors are paid $280,000 annually compared to only $90,000 for residents. Because it is

a teaching hospital a ratio of no more than three residents per teaching doctor must be maintained. The

hospital does not wish to fire any of its current employees and is only looking to hire new ones.

a.) What are your decision variables? Constraints? Graph the feasible region.

b.) How many new doctors and residents should the hospital hire to minimize the total annual

salary of the ICU? What is the salary budget needed for the ICU?

c.) Are any constraints redundant? If so which and why.

d.) Is the problem infeasible? Explain.

e.) Is the problem unbounded? If so, what real world constraint should be added?