Explain what the shadow price means in maximization problem

Explain what the shadow price means in maximization problem. Explain what this tells us from a management perspective.

Solution

Shadow price is defined as the estimated price of a good or service for which no market price exists.

In constrained optimization in economics, the shadow price is defined as the instantaneous change per unit of of the constraint. This is considered in the objective value of the optimal solution of an optimization problem obtained by relaxing the constraint.

To be more precise this can be taken as the marginal utility of relaxing the constraint or marginal cost of strengthening the constraint.

Suppose we have 3 products and the cost of increasing one unit for each product is the same, then shadow price is the increase in revenue due to increase of 1 unit.

Thus which gives maximum revenue is the optimum solution here.