A fast food restaurant uses full-time and part-time help to meet fluctuating demand during the day. The following table presents projected need for workers at different times of the day:
Time________________________ Workers needed
9:00 − 10:00...........................................4
10:00 − 11:00..........................................5
11:00 − 12:00..........................................9
12:00 − 1:00..........................................10
1:00 − 2:00.............................................8
2:00 − 3:00 ............................................4
3:00 − 4:00.............................................3
4:00 − 5:00.............................................6
There is a maximum of four full-time workers and the other workers are part-time workers. Each full-time worker is there from 9:00 until 5:00, while the part-time workers will work for 4 consecutive hours at a cost of $4.00 per hour. The cost of the full-time worker is $50 per day. The company wishes to minimize total cost while meeting the demands. Formulate this as a linear programming problem. Carefully define all decision variables.