True or false

______ If the reduced cost of a variable is 5, then the objective function coefficient of that variable needs to be reduced by 5 to make it attractive.

______ If an LP has multiple optimal solutions, then all solutions, even though different, will lead to the same objective function value (such as total profit or cost).

______ For a maximization LP problem, additional resource (increasing the RHS of a <= constraint) may improve the objective value. But for a minimization problem, additional resource may hurt the objective value.

______ The dual price for a <= constraint will increase or stay the same as you acquire more resources (increase the RHS).

______ While a dual price can be positive or negative, a reduced cost should always be non-negative in the LINDO output.

______ As long as all prices (objective coefficients) change within their respective ranges, the optimal solution of a linear program does not change.

______ If several RHS changes do not satisfy the 100% rule, then the dual prices of these constraints will change.

______ A linear program will always have a solution but sometimes the solution may consist of non-integers.

______ If a constraint is not tight then its dual price has to be zero. This conclusion is true for both >= and <= constraints.

______ It could happen that a small change in a RHS leads to neither the optimal solution change nor the objective function value change.

______ It could happen that a small change in an objective coefficient leads to neither the optimal solution change nor the objective function value change.