The National Science Foundation (NSF)

has received 4 proposals from professors to undertake new research in OR methods. Each proposal can be accepted for funding next year at the level (in thousands of dollars) shown in the following table or rejected. A total of $1 million is available for the year.

Proposal 1 2 3 4 Funding 700 400 300 600 Score 85 70 62 93 Scores represent the estimated value of doing each body of research that was assigned by NSF’s advisory panel.

(a) Formulate a discrete optimization model to decide what projects to accept to maximize total score within the available budget using decision variables xj = 1 if proposal j is selected and = 0 otherwise.

(b) Enter and solve your model with the class optimization software.