Ex$.4.$

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 at least 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$$ $,$ trained agent renting or teaching $600$$$,$ 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.