Reduced Cost
In a LINGO solution report, you’ll find a reduced cost figure for each variable. There are two valid, equivalent interpretations of a reduced cost.
First, you may interpret a variable’s reduced cost as the amount that the objective coefficient of the variable would have to improve before it would become profitable to give the variable in question a positive value in the optimal solution. For example, if a variable had a reduced cost of 10, the objective coefficient of that variable would have to increase by 10 units in a maximization problem and/or decrease by 10 units in a minimization problem for the variable to become an attractive alternative to enter into the solution. A variable in the optimal solution, automatically has a reduced cost of zero.
Second, the reduced cost of a variable may be interpreted as the amount of penalty you would have to pay to introduce one unit of that variable into the solution. Again, if you have a variable with a reduced cost of 10, you would have to pay a penalty of 10 units to introduce the variable into the solution. In other words, the objective value would fall by 10 units in a maximization model or increase by 10 units in a minimization model.
(按照这种解释走：就是说，是引入一个变量，每单位值必须付出的代价；当求最大值时，当引入单位变量时，目标函数值就会下降10.)
Slack or Surplus
The Slack or Surplus column in a LINGO solution report tells you how close you are to satisfying a constraint as an equality. This quantity, on less-than-or-equal-to (≤) constraints, is generally referred to as slack. On greater-than-or-equal-to (≥) constraints, this quantity is called a surplus. If a constraint is exactly satisfied as an equality, the slack or surplus value will be zero. If a constraint is violated, as in an infeasible solution, the slack or surplus value will be negative. Knowing this can help you find the violated constraints in an infeasible model—a model for which there doesn’t exist a set of variable values that simultaneously satisfies all constraints. Nonbinding constraints (constraints with a slack or surplus value greater than zero) will have positive, nonzero values in this column.
Dual Price
The LINGO solution report also gives a dual price figure for each constraint. You can interpret the dual price as the amount that the objective would improve as the right-hand side, or constant term, of the constraint is increased by one unit. Notice that "improve" is a relative term. In a maximization problem, improve means the objective value would increase. However, in a minimization problem, the objective value would decrease if you were to increase the right-hand side of a constraint with a positive dual price. Dual prices are sometimes called shadow prices, because they tell you how much you should be willing to pay for additional units of a resource. As with reduced costs, dual prices are valid only over a range of values. Refer to the LINGO|Range command in Windows Commands for more information on determining the
valid range of a dual price. For more information about modeling language see Intro to LINGO's Modeling Language section in Lingo Help.
