T or F

In an LP model, objective function and all constraints contain only terms involving decision variables raised to the first power

. An optimal solution to an LP model must occur at an extreme point which is located on the boundary of the feasible region

Solving an integer linear programming problem as a linear programming model and rounding the non-integer solution to integer values must result in a feasible solution.

FALSE

. In an LP model with two decision variables, the region that satisfies the constraint 4x1 + 15x2 ≥ 620 includes point (50, 10).

FALSE. At point (50, 10), the left-hand side value of the constraint is 4(50) + 15(10) = 350 which is not less than or equal to 620.

. In a feasible LP problem, an equal-to constraint (i.e., a constraint with = rather than ≤ or≥) can have a positive slack at the optimal solution.

FALSE. In a feasible LP problem, all constraints must be satisfied at the optimal solution. If there is an equal-to constraint in the model, then the LHS and RHS values of this constraint must be the same at the optimal solution. This means that the slack on this constraint must be equal to 0.

The standard form of an LP model requires all decision variables to be to the right and all numerical values to be to the left of the inequality or equality signs.

FALSE. In a standard LP model, all mathematical terms involving the decision variables are written to the left and the constant terms are written to the right of the inequality or equality signs

When using an LP model to solve the "diet" problem, the objective is generally to maximize nutritional content.

FALSE. In diet problems, the objective function is to be minimized and usually it is the cost. See A Minimization Problem lecture slides

Keeping all other factors the same, when a change in the value of an objective function coefficient is within the range of optimality, the value of the objective function remains the same.

FALSE. Keeping all other factors the same, when a change in the value of an objective function coefficient is within the range of optimality, the optimal solution remains the same

Sensitivity analysis should be performed before an optimal solution is found.

FALSE. Recall that sensitivity analysis is also called as post-optimality analysis, meaning that it is performed after an optimal solution is found.

Suppose (3;1) is a feasible solution of an LP problem with two decision variables. If the objective function of the problem changes while its constraints remain the same, then (3;1) is still a feasible solution in the new model

TRUE. Changing the coefficients of decision variables in the objective function does not change the constraints of the model. Therefore, the feasible region remains the same.

In an advertising media selection LP model, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the exposure.

TRUE. See LP Applications lecture slides.

8. The reduced cost for a decision variable whose value is positive at optimality must be zero.

TRUE

In order for an LP problem with two decision variables to have alternate solutions, the solutions must exist on the boundary of a non-redundant constraint parallel to the objective function line.

TRUE

The shadow price for a non-binding constraint will be zero if there is positive slack on this constraint.

TRUE. If a constraint is non-binding at the optimal solution, this constraint does not determine the optimal solution. Then, slightly increasing or decreasing the RHS value of this constraint does not change the optimal solution and so the value of the objective function at the optimal solution remains the same. This means that the shadow price for this constraint is 0.

If the right-hand side value of a binding constraint is changed, the feasible region will not be affected and will remain the same.

FALSE. A binding constraint forms the boundary of the feasible region, and so changing its right-hand side value affects the size of the feasible region.

A shadow price indicates how much a one-unit increase in the right-hand side value of a constraint will decrease or increase the optimal solution

FALSE. A shadow price indicates how much a one-unit increase in the right-hand side value of a constraint will decrease or increase the value of the objective function at the optimal solution.

At the optimal solution of an LP problem, a redundant constraint will have zero slack

FALSE. If the new value of the objective function coefficient is within its range of optimality, the optimal solution remains the same.