$(15$ points$)$ Consider the problem $of$ locating four machines along a straight aisle. Assume

that each machine$\frac{P}{D}$ point $is$ located $at$ the midpoint along the edge $of$ the machine work

area parallel $to$ the aisle. Let $c_{ij}=a_{ji}=1.$ The machine dimensions are $44$ for machine $1,33$

for machine $2,55$ for machine $3,$ and $22$ for machine $4.$ The loaded material handling

trips between machines are

Determine the best location $of$ machines along the aisle and the associated total cost.

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