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 4X13 + 25X14 + 22X23 + 3X24 - 3X34 - 3X43 - 20X35 - 30X36 - 40X37 - 6X45 - 15X46 - 20X47.
• MIN 4X13 + 25X14 + 22X23 + 3X24 - 3X34 - 3X43 - 20X35 - 30X36 - 40X37 - 6X45 - 15X46 - 20X47.
• MAX 4X13 + 25X14 + 22X23 + 3X24 + 3X34 + 3X43 + 20X35 + 30X36 + 40X37 + 6X45 + 15X46 + 20X47.
• MIN 4X13 + 25X14 + 22X23 + 3X24 + 3X34 + 3X43 + 20X35 + 30X36 + 40X37 + 6X45 + 15X46 + 20X47.