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$

What is the optimal solution to the Mantastic problem?

Group of answer choices

$$30,028$

$$30,820$

$$32,280$

$$32,820$