A company is involved in the production of two items (X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item:

                     Machine time    Craftsman time

        Item X           13                       20

        Item Y           19                       29

The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. Machine time is costed at  $10 per hour worked and craftsman time is costed at  $ 2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is $ 20 for X and $ 30 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer.

(a) Formulate the problem of deciding how much to produce per week as a linear program.
(b)Solve this linear program graphically.