If in a given feasible solution we have X$13=800,$ X$24=760,$ X$34=100,$ and X$43=0.$

A$.$ then X$35+$X$37$ must be equal to :

B$.$ then X$45+$X$45+$X$47$ must be equal to:

Mantastic Devices designs and manufactures high$-$end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at Memphis, New Orleans, or El Paso.

Manufacturing capacity in Manhattan and Atlanta is $900$ units each. Demand at Memphis, New Orleans, and El Paso is $450,500,$ and $610,$ respectively.

The network representing the shipping routes is shown below.

Memohis

The costs for shipping between each facility are shown below. A blank cell indicates th shipping between two facilities is not permitted.

$\backslash$table$[[,$Philadelphia,Knoxville,Memphis,New Orleans,El Paso$],[$Manhattan$,$$$4,$$$25,,,],[$Atlanta$,$$$22,$$$3,,,],[$Philadelphia$,,$$$3,$$$20,$$$30,$$$40],[$Knoxville$,$$$3,,$$$6,$$$15,$$$20]]$

Let $x_{13}=$ number of units shipped from node $1$ to node $3$ in the above network representation, with all other required variables similarly defined.