Give the objective function. Give all constraints, and be sure to write them in

Question

Give the objective function.

Give all constraints, and be sure to write them in standard form with only variables (with coefficients) on the left side of the equation or inequality and a constant (number) on the right side.

Be sure to define variables used.  

Note that we are NOT solving these problems using Excel.

A car dealership needs to make a schedule that includes part time employees and full time employees.

Full time employees are at the dealership for 9 hours, 8:00 AM to 5:00 PM, but take a 1 hour lunch break. The breaks are 11:00 – 12:00, 12:00- 1:00, or 1:00 – 2:00. 40% of the full time employees go to lunch at 11:00, 40% go at 12:00, and 20% go at 1:00.

Part time employees work 4 hours and do not get a break. Their shifts start at 9:00, 10:00, 11:00, 12:00 and 1:00.

Full time employees are paid $200 a day, and part time are paid $60 a day.

There can be a maximum of 20 full time employees, and at least 60% of the work-hours must be done by full time employees.

The table gives the number of employees needed for the different hours of the day.

Determine how many full time employees are needed and how many part time workers are needed per shift. Satisfy the constraints to minimize cost.

Hour Employees needed

8-9 15

9-10 18

10-11 20

11-12 25

12-1 23

1-2 20

2-3 18

3-4 16

4-5 19

Explanation / Answer

Hour Employees needed Full time 100% Full time 60% Lunch Break full time emp Part time 8-9 15 15 15 9-10 18 11 11 7 7 10-11 20 12 12 8 7 11-12 25 15 6 21 4 7 12-1 23 14 6 19 4 7 1-2 20 12 2 14 6 6 2-3 18 11 11 7 6 3-4 16 10 10 6 6 4-5 19 11 11 8 6 Number of working hours per full time employee 9 Number of working hours per part time employee 4 Cost of full time exmployes per day ######## Cost of part time employee per day $40.00 Maximum number of full time employees 20 Number of full time employee at any single hour is 605 of total labour reqd.

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