Madlantic Devices designs and manufactures high-end medical devices. The facilities in Madison 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 either Dayton, Bloomington, or Albany.
Manufacturing capacity in Madison and Atlanta is 1000 units. Demand at Dayton, Bloomington, and Albany is 450, 500, and 610, respectively.
The network representing the shipping routs is shown below.
The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted.

-The constraint for Philadelphia is
A) X13 + X23 - X35 - X36 - X37 = 0
B) X13 + X23 - X35 - X36 - X37 ≥ 0
C) X13 + X23 + X43 - X34 - X35 - X36 - X37 = 0
D) X13 + X23 + X43 - X34 - X35 - X36 - X37 ≥ 0

Question

Madlantic Devices designs and manufactures high-end medical devices. The facilities in Madison 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 either Dayton, Bloomington, or Albany.
Manufacturing capacity in Madison and Atlanta is 1000 units. Demand at Dayton, Bloomington, and Albany is 450, 500, and 610, respectively.
The network representing the shipping routs is shown below.
  The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted.
 
-The constraint for Philadelphia is
A) X13 + X23 - X35 - X36 - X37 = 0 
B) X13 + X23 - X35 - X36 - X37 ≥ 0 
C) X13 + X23 + X43 - X34 - X35 - X36 - X37 = 0 
D) X13 + X23 + X43 - X34 - X35 - X36 - X37 ≥ 0

Quizplus · Accepted Answer

The correct constraint for Philadelphia must account for all inflows and outflows to and from the city. The variables Xij represent the flow from city i to city j. For Philadelphia, which can be assumed to be city 3 based on the context, X13 and X23 represent inflows from cities 1 and 2, respectively, and X43 represents an inflow from city 4. The outflows are represented by X34 (to city 4), X35 (to city 5), X36 (to city 6), and X37 (to city 7). The equation must balance these inflows and outflows, hence the correct constraint is X13 + X23 + X43 - X34 - X35 - X36 - X37 = 0, indicating that the total inflow must equal the total outflow.

Madlantic Devices Designs and Manufactures High-End Medical Devices