Able 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 hiring and layoffs plan for 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 9,000 6,500 9,200

Salary & benefits cost per

Experienced consultant: $9,500 $9,500 $9,500 $9,500

New consultant: $6,000 $6,000 $6,000 $6,000

Able will have 44 experienced consultants that is, as defined by Able, consultants with six or more months of experience with Able present 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. Client project work must be done in the months shown.

Ables managing partner may choose to lay off up to 15% of the firms (still present) 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-months salary & benefit cost for that month. No newly hired consultants may be laid off over the four-month time period

Provide:

(a) a valid, properly-formatted linear algebraic formulation (model) for this scenario,

b) a readable screenshot of an optimized properly-formatted spreadsheet model [derived from the algebraic formulation (model) developed in part a] using Excel-Solver

(c) a clear written statement of the optimal solution [derived from the model of part b].