A certain linear program has the goal of maximizing the number of motors produced at the factory. One of the constraints in this program states that at most $40$ workers are available to work at the factory. The shadow price of this constraint is $8.$ What is the correct interpretation of this shadow price? $($Assume that the changes discussed stay within the appropriate RHS range.$)$

Group of answer choices

If the factory could find eight more workers, it could make one more motor.

If the factory hired an additional worker, its profit would increase by $$8.$

If the factory could find one additional worker, it could make eight more motors.

It would not be economical to hire additional workers for more than $$8.$

At most $48$ workers can work in the factory at a given time