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 12 20

Item Y 20 30

The company has 40 hours of machine time available in the next working week but only35hours of craftsman time. The revenue received for each item produced (all production is sold) isSh200 for X and Sh300 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer.

1. Formulate the problem to deciding how much to produce per week as a linear program. (4 marks)
2. Solve the linear program using graphical method.