An improvement in the value of the objective function per unit increase in the right-hand side of a constraint is the

The improvement in the value of the objective function per unit increase in the right-hand side of a constraint is known as the Shadow Price or Dual Value.

Here are the steps to understand this concept:

1. In linear programming, the objective function is what you are trying to maximize or minimize. For example, you might be trying to maximize profit or minimize cost.

2. The constraints are the limitations or restrictions that you have to work within. For example, you might have a limited amount of resources or time.

3. The right-hand side of a constraint is the value that the constraint must be less than or equal to. For example, if you have a constraint that says "the amount of resource A used must be less than or equal to 100", then 100 is the right-hand side of the constraint.

4. If you increase the right-hand side of a constraint, you are essentially loosening that constraint - you are allowing more of that resource to be used.

5. The shadow price or dual value is the amount by which the value of the objective function would increase if the right-hand side of the constraint were increased by one unit. In other words, it tells you how much more profit you could make (or cost you could save) if you had one more unit of that resource.

6. It's important to note that shadow prices are only valid within a certain range - if you increase the right-hand side of the constraint too much, the shadow price may change. This is because the optimal solution to the linear programming problem may change.