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 900 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 |
The objective function is:
• MAX 4X
13 + 25X
14 + 22X
23 + 3X
24 - 3X
34 - 3X
43 - 20X
35 - 30X
36 - 40X
37 - 6X
45 - 15X
46 - 20X
47.• MIN 4X
13 + 25X
14 + 22X
23 + 3X
24 - 3X
34 - 3X
43 - 20X
35 - 30X
36 - 40X
37 - 6X
45 - 15X
46 - 20X
47.• MAX 4X
13 + 25X
14 + 22X
23 + 3X
24 + 3X
34 + 3X
43 + 20X
35 + 30X
36 + 40X
37 + 6X
45 + 15X
46 + 20X
47.• MIN 4X
13 + 25X
14 + 22X
23 + 3X
24 + 3X
34 + 3X
43 + 20X
35 + 30X
36 + 40X
37 + 6X
45 + 15X
46 + 20X
47.
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