A flooring company is involved in fitting two types of floorings (X and Y). The resources needed to finish X and Y are twofold, Singapore

Question 1

A flooring company is involved in fitting two types of floorings (X and Y). The resources needed to finish 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 square meter of floorings:

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 £100 per hour worked and craftsman time is costed at £20 per hour worked. Both machine and craftsman idle times incur no costs. The revenue per square meter received for each type of floor produced is £200 for X and £300 for Y. The company also has a specific contract to fit 10 square meters of X per week for a particular client“ABC”.

1. Formulate the problem of deciding how much to fit per week for each type of floor X and Y as a linear program and solve this linear program graphically.
2. Discuss how the results obtained in ‘a’ can be changed when the contract with the client “ABC” is expired.