Here is the problem i need to form (not solve) a model for a linear programming problem .
A major airport is reviewing their staffing needs for air traffic controllers. The most recent labor agreement has specified hiring for eight different shifts consisting of eight hours per shift. FAA regulations specify that air controllers work 2-hour intervals with an hour break between.
Airport officials specify that each controller work the first 2 hours of a shift. The following figure illustrates the hours of each shift and the periods during which a controller is on duty. airport officials have determined the minimum number of controllers on duty for each hour of the day. These are also indicated in the figure
The base pay per controller is $80 per shift with differentials for certain shifts. Any shifts beginning between 4 p.m. and 11 p.m.are paid at a 10 percent premium for the entire shift; and any beginning between midnight and 6 a.m. receive a 20 percent premium.
Airport officials want to determine the number of controllers to hire for each shift so as to meet the hourly requirements at a minimum cost per day. Formulate an appropriate model. (You do NOT need to solve this LP)
The way I read the problem is that there are 8 shifts and you must have the maximum minimum amount of workers for each time period , but It says all workers must do the first 2 hours of a shift , so does this mean they can work 2 hours leave then come back for the last hour and be paid for only 3 hours , I don't really have any idea on how to begin turning this into a model since there are no constraints only a desire for minimum costs