Use the following problem statement to answer questions $1-6.$

The LMN Company is a distributor of products. The network model below shows the shipping costs, supply, demand, and shipment routes between each source and destination. The distribution centers are in Philadelphia and Knoxville. Shipments are prohibited from Atlanta to Philadelphia due to a shortage of drivers. The company wants to determine the optimal shipments from plants to retail outlets to minimize total transportation cost. $[$Note: Xij $=$ number of products shipped from source i to destination j$.]$

$14$ points

Which of the following constraints is correct?

$7x13+5141500$

$x13+x141500$

$24$ points

Which constraint represents the quantity shipped to New Orleans?

$636+546=500$

$x36+x46=400$

$3$

$4$ points

Which constraint represents transshipment through the distribution centers?

$x35+x36+x37=x45+x46+x47$

$x14+x24=x45+x46+x47$