Westside Technology Consulting is an information technology consulting firm based in Los Angeles, California. The firm is owned by two engineers with extensive experience in the hardware design field who are able to act as lead engineers on consulting projects, as are two other members of the firm. Westside also employs 9.5 other engineering staff members (one works only half time) and 15 electronics technicians. Westside works on projects which can be classified into one of three categories: major design projects, trouble-shooting projects, and hourly contract work. Major design projects typically require one lead engineer, three staff engineers, and four technicians. Trouble-shooting projects require one lead engineer, two staff engineers, and two technicians. Hourly contract work utilizes one staff engineer and one technician.
Major design contracts run on a yearly basis and net the firm $100,000 each after costs. The owners have established a policy to have at least two major contracts in place each year to stabilize cash flow. Trouble shooting contracts are generally signed on a quarterly basis and net the firm $60,000 each. Hourly contract work earns a net of $50 per hour, assuming a 40 hour work week for 52 weeks.
Westside's research lab has limited space. A major project will take up to 2,400 sq. ft., and a trouble-shooting contract typically requires 1,500 sq. ft. A total of 7,000 sq. ft. of research lab space is available. Hourly contract work is carried out primarily at the client location, however, some tasks are performed at the lab, requiring 500 sq. ft. of lab space. The owners wish to plan the contract placement for the next year and need to determine if the available work force can be efficiently structured for the contract load.
a. Formulate an appropriate linear programming model that can be used to determine the optimal contract structure for the next year.
b. Determine the optimal contract structure using the Management Scientist software, including the number of contracts of each type to be placed and the total contribution to profit. Provide a narrative that explains the Management Scientist solution used.
c. Evaluate the current work force capacity, assuming that Westside intends to operate at this level for an extended period of time. Provide
a narrative of the Management Scientist solution information used.