The firm of Miller, Lombardi, and York was recently formed by the merger of two companies providing accounting services. York's business was providing personal financial planning; Miller and Lombardi conducted audits of small governmental units and provided tax planning and preparation for several commercial firms. The combined firm has leased new offices and acquired several microcomputers that are used by the professional staff in each area of service. However, in the short run, the firm does not have the financial resources to acquire computers for all the professional staff.
The expertise of the professional staff can be divided into three distinct areas that match the services provided by the firm-tax planning and tax return preparation, insurance and investments, and auditing. Since the merger, the new firm has had to turn away business in all three areas of service. One of the problems is that although the total number of staff seems adequate, the staff members are not completely interchangeable. Limited financial resources do not permit hiring new staff in the near future, and, therefore, the supply to staff is restricted in each area.
R. Oliva has been assigned the responsibility of allocating staff and computers to the various client engagements. Management wants Oliva to maximize revenues in a manner consistent with maintaining a high level of professional service in each of the areas of service. Management's time is billed at $100 per hour, and the staff's time is billed at $70 per hour for those with experience, and $50 per hour for inexperienced staff. P. Wren, a member of the staff, recently completed a course in quantitative methods at the local university. Wren suggested to Oliva that linear programming could be used to allocate appropriate staff and computers to the various assignments.
Required:
(1) Identify and discuss the primary assumption underlying the linear programming model.
(2) Explain why linear programming is appropriate for making staff assignments.
(3) Identify the data needed to develop a linear programming model for the company.
(4) List objectives other than revenue maximization that R. Oliva should consider before making staff allocations.