When using Linear Programming solving optimization problems.

The objective goal could influence the meaning of shadow price and reduced the cost of the decision variables and constraints?

For example, for profit-maximization problem. We say the reduced cost is 1 for X1. We say, increasing one unit of X1 will bring down the profit by 1 dollar. When the shadow price of binding constraint C1 is 2. We say adding one additional unit of C1 will increase the 2 dollar profit.

When it cost to cost minimization, how do we interpret the reduced cost and shadow price?