1. Human resources planning problem A rent-a-car company operates a rental-agent training program, which students com- plete 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 150 160 June 180 April 170 May 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/teaching $600 Trained agent idle $500 Company policy forbids firing because of an excess of agents. (a) Formulate and solve 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 that an unlimited supply of students exists. Assume also that in June the training school closes for vacation.