NYNEX Must Schedule Round-The-Clock Coverage for Its Telephone Operators Formulate This Scheduling Decision as a Linear Programming Problem,defining Fully

NYNEX must schedule round-the-clock coverage for its telephone operators.To keep the number of different shifts down to a manageable level,it has only four different shifts.Operators work eight-hour shifts and can begin work at either midnight,8 a.m.,noon,or 4 p.m.Operators are needed according to the following demand pattern,given in four-hour time blocks.
$$\begin{array} { | l | c | } \hline \text { Time Period } & \text { Operators Needed } \\\hline \text { midnight to } 4 \text { a.m. } & 4 \\\text { 4 a.m. to } 8 \text { a.m. } & 6 \\8 \text { a.m. to noon } & 90 \\\text { Noon to } 4 \text { p.m. } & 85 \\\text { 4 p.m. to } 8 \text { p.m. } & 55 \\\text { 8 p.m. to midnight } & 29 \\\hline\end{array}$$
Formulate this scheduling decision as a linear programming problem,defining fully your decision variables and then giving the objective function and constraints.