Network flow model for the furniture manufacturing problemA furniture manufacturer has warehouses in cities represented by nodes $1,2,$ and $3$ in Figure $5\mathrm{.}37.$ The values on the arcs indicate the per unit shipping costs required to transport living room suites between the various cities. The supply of living room suites at each warehouse is indicated by the negative number next to nodes $1,2,$ and $3.$ The demand for living room suites is indicated by the positive number next to the remaining nodes. Identify the supply, demand, and transshipment nodes in this problem.

Which of following solution is not possible as per information given in problem?

Group of answer choices

$20$ from $3$ to $1,10$ from $4$ to $2,30$ from $5$ to $2,40$ from $6$ to $3$

$30$ from $1$ to $4,20$ from $4$ to $6,20$ from $3$ to $6,30$ from $2$ to $5$

$20$ from $1$ to $3,10$ from $2$ to $4,30$ from $2$ to $5,40$ from $3$ to $6$

$40$ from $2$ to $5,10$ from $5$ to $6,20$ from $3$ to $6,10$ from $4$ to $6,20$ from $1$ to $4$

Which of following solution violate demand and supply constraint?

Group of answer choices

$20$ from $1$ to $3,10$ from $2$ to $4,30$ from $2$ to $5,40$ from $3$ to $6$

$30$ from $1$ to $4,20$ from $4$ to $6,20$ from $3$ to $6,30$ from $2$ to $5$

$40$ from $2$ to $5,30$ from $5$ to $6,20$ from $3$ to $4,10$ from $4$ to $6$

$40$ from $2$ to $5,10$ from $5$ to $6,20$ from $3$ to $6,10$ from $4$ to $6,20$ from $1$ to $4$

What is least costly shipping plan for this problem?

Group of answer choices

$30$ from $1$ to $4,20$ from $4$ to $6,20$ from $3$ to $6,30$ from $2$ to $5$

No optimal solution possible for this problem

$40$ from $2$ to $5,10$ from $5$ to $6,20$ from $3$ to $6,10$ from $4$ to $6,20$ from $1$ to $4$

$20$ from $1$ to $3,10$ from $2$ to $4,30$ from $2$ to $5,40$ node $3$ to $6$

What is the least shipping cost for this problem?