$1.$ Goal Programming problem The L$.$ Young & Sons Manufacturing Company produces two products, which have the following profit and resource requirement characteristics: Last month$$s production schedule used $350$ hours of labor in department A and $1000$ hours of labor in department B$.$ Young$$s management has been experiencing workforce morale and labor union problems during the past six months because of monthly departmental workload fluctuations. New hiring, layoffs, and interdepartmental transfers have been common because the firm has not attempted to stabilize workload requirements. Management would like to develop a production schedule for the coming month that will achieve the following goals: Goal $1$: Use $350$ hours of labor in department A$.$ Goal $2$: Use $1000$ hours of labor in department B$.$ Goal $3$: Earn a profit of at least $$1300.$