Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2.

Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units.
-Which constraint represents the quantity shipped to retail outlet 6?
A) X23 + X36 = 450
B) X23 + X36 + X26 = 450
C) X36 + X26 ≤ 450
D) X36 + X26 = 450
E) 3X36 + 5X26 = 450

Question

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2.

Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units.
-Which constraint represents the quantity shipped to retail outlet 6?
A) X23 + X36 = 450 
B) X23 + X36 + X26 = 450 
C) X36 + X26 ≤ 450 
D) X36 + X26 = 450 
E) 3X36 + 5X26 = 450

Quizplus · Accepted Answer

The constraint for the quantity shipped to retail outlet 6 is represented by the arc connecting node 3 (the distribution center) and node 6 (retail outlet 6), which is X36 + X26 = 450. This is because the only possible routes for supplying retail outlet 6 are through the distribution center from either plant 2 (X26) or from the direct shipment from plant 3 (X36). Option A only represents the direct shipment from plant 3 to outlet 6, option B includes an additional arc that is not relevant to outlet 6, option C does not take into account the shipment from plant 2, and option E includes coefficients that are not present in the provided network. Therefore, option D is the best choice.

Consider the Following Network Representation of Shipment Routes Between Plants