A rent-a-car company operates a rental-agent training program, which students complete in one month. The teachers in this program are trained rental agents, at a ratio of one for every fifteen students. Experience has shown that twenty-five students must be hired for every twenty who successfully complete the program. The demand for rental cars is seasonal and, for the next six months, requires rental agents as follows:
January 135
February 125
March 150
April 170
May 160
June 180
As of 1 January, 145 trained rental agents are available for counter work or teaching, and the personnel records indicate that 8% of the trained rental agents leave the company at the end of each month. Payroll costs per month are:
Student $350, Trained agent renting of teaching $600, Trained agent idle $500
Company policy forbids firing because of an excess of agents.
Formulate a linear program that will produce the minimum-cost hiring and training schedule that meets the
demand requirements, assuming that average labor turnover rates prevail and ignoring the indivisibility of agents. Assume also that in June the training school closes for vacation.