The Temporary Help Company must provide secretaries to its clients over the next year on the following estimated schedule: spring, 6000 secretary-days; summer, 7500 secretary-days; fall, 5500 secretary-days; and winter, 9000 secretary-days. A secretary must be trained for 5 days before becoming eligible for assignment to clients.
There are 65 working days in each quarter, and the beginning of the spring season there are 120 qualified secretaries on the payroll. The secretaries are paid by the company and not the client; they earn a salary of $800 a month. During each quarter, the company loses 15% of its personnel (including secretaries trained in the previous quarter).
Formulate the problem as a linear-programming problem. (Hint: Use xt as the number of secretaries hired at the beginning of season t, and St as the total number of secretaries at the beginning of season t.)