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# Linear Program to estimate the number of hours of casework

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The law firm of Smith, Smith, Smith, and Jones is recruiting at law schools for new layers 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 moth ofr the following year:

Month casework(hr.) month casework (hr.)
january 650 july 750
february 450 august 900
march 600 steptember 800
april 500 october 650
may 700 november 700
june 650 december 500

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.

52. In problem 51 the optimal solution results in a fractional 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 resuls between this new solution and the optimal non-integer solution obtained in problem 51.