A large local dinner is open each weekday from 6am until 8pm. Each waitstaff begins his/her shift 6-hour shift either at 6am, 8am, 10 am, noon or 2pm. To determine how many waitstaff should begin at each of the above 5 times, the owner, based on her knowledge of her customers, has determined the minimum number of waitstaff that is required during each 2- hour time slot to give her customers the service that they expect. This information, along with the wages** that are paid to each waitstaff for the 6-hour shift that they work, appears in the following table.

Time slot minimum required wages for 6-hour shift **

6am 8am 5 $85

8am 10am 6 $60

10am noon 15 $85

noon 2pm 11 $70

2pm 4pm 5 $65

4pm 6pm 6 -----

6pm - 8pm 4 -----

** Each wage per shift is based on when the waitstaff starts his/her shift. For example, the $70 listed for the 6am 8am time slot is the wages for those starting at 6am, and, the $60 listed for the 8am 10am time slot is the wages for those starting at 8am, etc., etc.

Note: No shifts start at 4pm or 6pm because they would not be able to work a full 6-hour shift

Using X₁, X₂, , X₅, to represent the number of waitstaff starting at 6am, 8am, , 4pm, formulate what is being asked for so that the owner can minimize her daily wages while satisfying all her minimum requirements. No s are to be used anywhere in your formulations.

1. the objective function

2. the constraint for the 6am 8am time slot

3. the constraint for the noon 2pm time slot

4. the constraint for the 4pm 6pm time slot

5. the constraint for the 6pm 8pm time slot