1- 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 either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and

Atlanta is 800 units. Demand at Memphis, New Orleans, and El Paso is 450, 500, and 610, respectively.

The network representing the shipping routes 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.

Philadelphia Knoxville Memphis New Orleans El Paso

Manhattan $4 $25

Atlanta $22 $3

Philadelphia $3 $20 $30 $40

Knoxville $3 $6 $15 $20

i) What is the objective function for the Mantastic problem? Use the notation , where and correspond

to the node numbers indicated in the diagram.

ii) What is the constraint for the transshipment node in Philadelphia for the Mantastic problem?