Radom Manufacturing produces various products. The company operates a landfill, which it uses to dispose of nonhazardous trash. The trash is hauled from the two nearby manufacturing facilities in trucks that can carry up to five tons of trash in a load. The landfill operation requires certain preparation activities regardless of the amount of trash in a truck $($i$.$e$.,$ for each load$).$ The budget for the landfill for next year follows:

Volume of trash $2,450$ tons $(490$ loads$)$

Preparation costs $($varies by loads$)$ $ $166,600$

Other variable costs $($varies by tons$)166,600$

Fixed costs $245,000$

Total budgeted costs $ $578,200$

Radom plans to make the landfill a profit center and charge the manufacturing plants for disposal of the trash. The landfill has sufficient capacity to operate for at least the next $20$ years. Other landfills are available in the area $($both private and municipal$),$ and both Radom manufacturing plants would be free to decide which landfill to use.

Required:

Compute the optimal transfer price.

Compute the total variable costs for a three$-$ton load of trash from one of the plants.