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.

1.Formulate this problem as a linear programme.

2. Use a graphical method to find an optimal solution.

3. Use a suitable program to check your results.