Mama’s Kitchen serves from 5:30 a.m. each morning until 1:30 p.m. Tables are set and cleared by busers working 4-hour shifts beginning on the hour from 5 a.m. through 10 a.m. Most are college students who hate to get up in the morning, so Mama’s pays $7 per hour for the 5, 6, and 7 a.m. shifts, and $6 per hour for all others. The manager seeks a minimum cost staffing plan that will have 2 busers on duty for the hour beginning at 5 a.m., plus 3, 5, 5, 3, 2, 4, 6 and 3 on duty for the hours to follow.

(a) Formulate a shift scheduling LP to select an optimal staffing plan.

(b) Which of the constraints of your model are covering constraints? Explain.

(c) Enter and solve your model with the class optimization software.