Math/Management
posted by Carla on .
Ten jobs are to be completed by three workers (Sam, Joy, and Kelly) during the next
week. Each person works a 40hour week and is paid an hourly rate: Sam, Joy, and Kelly
earn $11, $13, and $14 per hour, respectively. Union rules require workers to be treated
fairly; to ensure that most of the work is not assigned to one person while others are too
idle, make sure that no person works more than 8 hours above any other worker. For
example, if Joy works 20 hours, then Sam and Kelly should work within 12 to 28 hours,
and Sam and Kelly should have workhours that are no more than 8 hours apart.
The times for the workers to complete the tasks are shown in the table below. The values
in the cells assume that each task is completed by a single person. However, tasks can be
shared with completion times being determined proportionally (e.g. if Joy and Kelly
share task 1 equally, then Joy works 6 hours and Kelly works 9 hours). If no entry exists
in a particular cell, it means that task cannot be performed by that worker.

a. Formulate the problem as a linear programming model (that is, define the variables,
and write down the objective function and all constraints mathematically).
b. Create a spreadsheet model for this problem and solve with Excel Solver.
c. What is the optimal solution? What is the optimal value?