Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 39

In Problem, the optimal solution results in a fractional (i.e., non-integer) number of lawyers being hired. Explain how you would go about logically determining a new solution with a whole (integer) number of lawyers being hired and discuss the difference in results between this new solution and the optimal non-integer solution obtained in Problem.
Problem
The law firm of Smith, Smith, Smith, and Jones is recruiting at law schools for new lawyers for the coming year. The firm has developed the following estimate of the number of hours of casework it will need its new lawyers to handle each month for the following year:
Each new lawyer the firm hires is expected to handle 150 hours per month of casework and to work all year. All casework must be completed by the end of the year. The firm wants to know how many new lawyers it should hire for the year.
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.