Weekly production schedules are needed for the manufacture of two products X and Y. Each unit of X uses one component made in the factory, while each unit of Y uses two of the components, and the factory has a maximum output of 80 components a week. Each unit of X and Y requires 10 hours of subcontracted work and agreements have been signed with subcontractors for a minimum weekly usage of 200 hours and a maximum weekly usage of 600 hours. The marketing department says that all production of Y can be sold but there is a maximum demand of 50 units of X, despite a long-term contract to supply 10 units of X to one customer. The net profit on each unit of X and Y is $200 and $300 respectively. Formulate a linear programming model for this problem first and then solve this model by using graphical method.