$1.(15$ points$)$ Consider the problem of locating four machines along a straight aisle. Assume that each machine P$/$D point is located at the midpoint along the edge of the machine work area parallel to the aisle. Let cij $=$ aij $=1.$ 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

$$

$1$

$2$

$3$

$4$

$1$

$-$

$10$

$2$

$15$

$2$

$8$

$-$

$5$

$4$

$3$

$2$

$4$

$-$

$9$

$4$

$10$

$5$

$9$

$-$

$$

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