Reference no: EM132242394

Provide algebraic formulation and optimal solution:

Amy Consultants, a firm specializing in short-term financial analysis assistance, is facing a shortage of personnel over the next four months and would like to determine the lowest-possible-cost solution to meeting their commitments to clients. The required monthly hours on clients’ consulting projects, and expected salary & benefits cost per consultant by month are as follow:

                                                                          May               June             July               August

    Required hours for client projects:                 8,000            7,000            7,500            9,200

    Salary & benefits cost per consultant:           $7,500           $7,000          $6,700          $6,700

Amy will have 35 experienced consultants – that is, as defined by Amy, consultants with six or more months of experience with Amy– on staff at the end of April. New consultants can be hired at the beginning of each of the upcoming four months, but, though they put in the same time as the experienced consultants (i.e., 195 hrs. per month), they are only half-productive with their work time in their first month. Also, in their first month, new consultants must spend 30 hrs. with experienced consultants in one-on-one orientation activities, keeping both parties from doing any client project work during those hours.

firm's managing partner may layoff up to 15% of the experienced consultants at the beginning of any month, but those laid off at the beginning of a month are paid the equivalent of a half-month’s salary & benefit cost for that month.