$10\mathrm{.}29$ Six cells $(20$

$20$

$)$ are to be located in a $2$

$3($rectangular$)$ facility, as shown in the

figure below. The material flow matrix is given in a separate table. The material han$-$

dling cost is directly proportional to the distance traveled $($from centroid to centroid$).$

Assume rectilinear distance.

a$.$ Determine a lower bound for the material handling cost.

b$.$ Given an initial cell layout where product $1$ is located in cell A$,$ product $2$ is located

in cell B$,$ etc., calculate the total material handling cost.

c$.$ Use the improvement procedure to determine a better layout and calculate its total

material handling cost.