The table below shows the number of trips between each pair of four machines and the dimension requirements of the machines.

The dimensions of the shop floor are 635 m.

Machine\Machine 1 2 3 4

Dimensions (m) 1 - 15 9 3 48 2 - 8 0 57 3 - 6 69 4 - 48

(50 pts) Formulate the LP model of the layout problem by using the minimum number of decision variables. (Define the decision variables, set up the objective function clearly and express each constraint separately by using the data provided. A generic formulation will not be graded!)

b) (10 pts) Formulate constraint(s) that guarantee that machines 1 and 2 are not adjacent?

c) (10 pts) Formulate constraint(s) that guarantee that machines 3 and 4 are adjacent? d) (30 pts) Propose a relationship diagram and develop a layout.