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Jane MacFarlane wants a weekly schedule for two business services, X and Y. Each ‘unit' of X delivered to customers needs one service package, while each unit of Y uses two of the packages, and Jane has a maximum of 80 packages available a week. Each unit of X and Y needs 10 hours of subcontracted work, and Jane has signed agreements with subcontractors for a weekly minimum of 200 hours and a maximum of 600 hours. Jane knows from market surveys that demand for Y is high, and she will have no trouble selling any number of units. However, there is a maximum demand of 50 units of X, despite a long-term contract to supply 10 units to one customer. The net profit on each unit of X and Y is €2,000 and €3,000 respectively. Formulate this problem as a linear programme. Use a graphical method to find an optimal solution. Use a suitable program to check your results.
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