No.5. Shortly find the mathematical expression of Lagrangian multiplier of “constrained revenue maximization”, “constrained output maximization” and “cost minimization subject to revenue constraint”...

No.5.
Shortly find the mathematical expression of Lagrangian multiplier of “constrained revenue maximization”, “constrained output maximization” and “cost minimization subject to revenue constraint” then find the mathematical expression of:

(a) relationship between Lagrangian multiplier of “constrained revenue maximization” and “constrained output maximization”

(b) relationship between Lagrangian multiplier of “constrained revenue maximization” and “cost minimization subject to revenue constraint”