Quiz 3

A systematic approach to an LP model formulation is to first construct the objective function before defining the decision variables

FALSE. The first step is to define the decision variables. See the formulation of the Toys & Boys problem on slides #13-14 of Introduction to LP lecture slides.

The graph of a linear inequality constraint consists of a line and some points on both sides of the line.

FALSE. The graph of a linear inequality constraint consists of a line and some points on only one side of the line.

7. The solution to an LP problem must always lie on the boundary of a constraint.

FALSE. This statement would be true if it was "The optimal solution to an LP problem must always lie on the boundary of a constraint.

. When formulating an LP model on a spreadsheet, the objective function is located in the target cell.

TRU

The optimal solution to a maximization LP problem with two decision variables can be found by graphing the feasible region and finding the profit at every corner point of the feasible region to see which one gives the largest value.

TRUE

If an LP model with two decision variables has a solution at all, it will have a solution at some corner of the feasible region.

TRUE. An optimal solution to an LP model must occur at an extreme point which is actually a corner point of the feasible region.

No point in the interior of the feasible region can be an optimal solution to an LP problem.

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

The following is a valid objective function for a linear programming problem: Minimize 4x1 + 3x2 +(2/3)x3

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

A feasible solution point in an LP model with two decision variables does not have to lie on the boundary of the feasible region

TRUE. It can be an interior feasible point. See types of feasible points on slide #16 of A Graphical Analysis of LP lecture slides.

17. An LP problem can have more than one optimal solution.

TRUE. See "alternate optimal solutions" on A Graphical Analysis of LP lecture slides.

9. In any LP problem, all model parameters are assumed to be known with certainty.

TRUE. See certainty assumption on slide #7 of Introduction to LP lecture slides.

If the addition of a constraint to an LP model does not change the feasible region, the constraint is said to be redundant.

TRUE. See on slide #11 of A Graphical Analysis of LP lecture slides.

In linear programming, when we say that proportionality exists, we mean that if one unit of a product requires two units of a resource, then three units of the product must require six units of the resource.

TRUE. See proportionality assumption on slide #7 of Introduction to LP lecture slides.

13. The point (3, 2) satisfies the constraint 2x1 + 6x2 ≤ 30.

TRUE. When x1 = 3 and x2 = 2, the left-hand-side value of the constraint is 2(3) + 6(2) = 18 and this value is strictly less than the right-hand-side value of the constraint.

Non-binding constraints are not associated with the feasible region. That is to say, they are redundant and can be eliminated from consideration.

FALSE. A non-binding constraint forms one part of the feasible region. It is called a non-binding constraint because the optimal solution is not located on the boundary of that constraint

Adding a constraint to an LP problem increases the size of the feasible region

FALSE. Adding a constraint to an LP problem always decreases the size of the feasible region (unless it is a redundant constraint). If it is a redundant constraint, then it does not affect the feasible region. In either case, it never increases the size of the feasible region.

An LP problem with any number of decision variables can be solved by using the graphical solution procedure.

FALSE. Graphical solution method can be used to solve only LP models with two decision variables.

In linear programming, if a constraint has a slack that is not equal to zero at optimality, it is referred to as a binding constraint

FALSE. If a constraint has a non-zero slack at optimality, that constraint is called a non-binding constraint.

. In an LP model, the constraints must be linear, but the objective function may be non-linea

FALSE. In an LP model, objective function and all constraints must be linear.

8. In an LP model, an infeasible solution must violate all constraints of the problem.

FALSE. In an LP problem, a solution is infeasible if it violates at least one constraint.