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 objective function is:
A) MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47
B) MIN 7X13 + 8X14 + 4X23 + 7X24 - 3X34 - 3X43 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47
C) MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 - 25X35 - 6X36 - 17X37 - 29X45 - 8X46 - 5X47
D) MIN 7X13 + 8X14 + 4X23 + 7X24 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47

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 objective function is:
A) MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47 
B) MIN 7X13 + 8X14 + 4X23 + 7X24 - 3X34 - 3X43 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47 
C) MIN 7X13 + 8X14 + 4X23 + 7X24 + 3X34 + 3X43 - 25X35 - 6X36 - 17X37 - 29X45 - 8X46 - 5X47 
D) MIN 7X13 + 8X14 + 4X23 + 7X24 + 25X35 + 6X36 + 17X37 + 29X45 + 8X46 + 5X47

Quizplus · Accepted Answer

The objective function is a linear combination of the shipping costs (coefficients) and the decision variables (Xij), where i represents the starting facility and j represents the ending facility. The objective is to minimize the total shipping cost. Option A represents the correct formulation of the objective function, with all relevant terms included. Option B is incorrect because it introduces negative coefficients for some terms, which does not make sense in this context. Option C is also incorrect because it introduces negative coefficients and flips the sign of all terms related to shipping from Philadelphia and Knoxville, which again does not make sense. Option D is incomplete because it only includes the terms for shipping from Madison and Atlanta, but not for shipping to final assembly facilities.

Madlantic Devices Designs and Manufactures High-End Medical Devices