A car manufacturing facility main line is used to produce three models, outputting N1, N2, N3 vehicles a day for each of three models. Each vehicle can then either be shipped to customer as is (standard configuration) or can be first customized to one of four advanced configurations: premium, limited, sport, special. Profit for each vehicle depends on the model and configuration, and is given by value rij, where i is one of three models and j is one of five configurations. Further, aij gives the man-hours required to customize a vehicle of model i to configuration j. Each day there are M man-hours available for customization. Further, up to Q additional overtime man-hours can be scheduled at cost c per hour. Required:
Formulate Linear programming (objectif function and constraint) with an explanation.