$[-/20$ Points$]$

CAMMIMS$166.$E$\mathrm{.}023.$

ASK YOUR TEACHER

Consider the following transshipment network for finding the shortest route from node $1$ to node $7.$

$($a$)$ Formulate a linear programming model of the problem. $($Express your answers using $x_{ij},$ where each $x_{ij}$ is either $0$ or $1$ for the arc from node $i$ to node $j.)$

Min

s$.$t$.$

Node $1$ Flows

Node $2$ Flows

Node $3$ Flows

Node $4$ Flows

Node $5$ Flows

Node $6$ Flows

Node $7$ Flows

For all $x_{ij}=0,1.$

$($b$)$ Find the shortest route from node $1$ to node $7$ in the network shown. $($Enter your answers as a comma$-$separated list.$)$ path $=1,,7[-/20$ Points$]$

CAMMIMS$166.$E$\mathrm{.}035.$

ASK YOUR TEACHER

PRACTICE ANOTHER

Contois Carpets is a small manufacturer of carpeting for home and office installations. Production capacity, demand, production cost per square yard $($in dollars$),$ and inventory holding cost per square yard $($in dollars$)$ for the next four quarters are shown in the network diagram below. Capacities $($arcs$)$

$($i$)$

Develop a linear programming model to minimize cost and meet demand exactly. $($Let $x_{ij}$ be the number of square yards of carpet which flows from node $i$ to node $j.)$

Min