A ﬁrm produces two different models of heavy machines; say (A) and (B). The market demand implies that the ﬁnal proﬁt of each model is 1200 and 2500, respectively. The production of each car (of both models) is organized in three diﬀerent factories (engine, (E), skeleton (S), complements (C)). The following table explain the days needed for each model in each factory to produce the cars: (A,E)=2, (A,S)=1, (A,C)=1, (B,E)=4, (B,S)=4, (B,C)=7
Because of safety reasons and the agreements between the company and the workers, the engine factory is open no more than 350 days per a year, the skeleton factory is open no more than 280 days per a year while complements factory may work up to 320 days per a year. Find the linear program to optimize the proﬁts, and solve it. Write the dual problem. Is it possible to determine the shadow prices of the three factories?