Linear Programming

The department estimates that 500 hours will be required to complete the project. However, only four members are available for the research and they are Ben, Wilson, Messi and Elsa . Because Ben and Wilson are the supervisors of he project, they must be assigned at least 70% of the total number of hours. To provide research experience for Elsa , Elsa must be assigned at least 15% of the total project time. However, due to other departmental duties and responsibilities, Messi has a maximum of 30 hours available to work on this project. Hourly wage rates are $50 for Ben, $45 for Wilson, $45 for Messi and $20 for Elsa .

Denote
B = number of hours assigned to Ben
W = number of hours assigned to Wilson
M = number of hours assigned to Messi
E = number of hours assigned to Elsa
a) Formulate a linear program that can be used to determine the number of hours
each member should be assigned to the project in order to minimize total cost.