Question 1

Which of the following is not a property of all linear programming problems?

Accepted Answer

While linear programming problems often involve the use of a computer program to facilitate optimization, it is not a necessary property of all linear programming problems. The presence of restrictions, optimization of some objective, and alternate courses of action are all fundamental aspects that define a linear programming problem.

Question 2

In a minimization problem, the isocost line is used rather than an isoprofit line.

Accepted Answer

In a minimization problem, the objective is to minimize costs rather than maximize profits, so the isocost line (which represents all possible combinations of inputs that yield a given total cost) is used to determine the optimal input levels. The use of an isoprofit line would be irrelevant in such a scenario.

Question 3

The addition of a redundant constraint lowers the isoprofit line.

Accepted Answer

The addition of a redundant constraint does not affect the position of the isoprofit lines, as these lines are determined by the objective function coefficients, not by the constraints. Redundant constraints do not change the feasible region or the optimal solution.

Question 4

Which of the following is not a part of every linear programming problem formulation?

Accepted Answer

A redundant constraint is not always present in every linear programming problem formulation. Redundant constraints are those that do not affect the feasible region and can be removed without affecting the solution.

Question 5

When two or more constraints conflict with one another, we have a condition called unboundedness.

Accepted Answer

When two or more constraints conflict with one another, we have a condition called infeasibility, not unboundedness. Unboundedness refers to a situation where the objective function can be maximized or minimized without any limit.

Question 6

If you enter inequalities such as "≤" directly into your Excel spreadsheet, you do not need to designate them when defining constraints using Solver.

Accepted Answer

When defining constraints in Solver, you must specify the type of inequality (e.g., ≤, ≥, =) for each constraint through the Solver Parameters dialog box; simply entering these symbols directly into cells does not automatically apply them as constraints in Solver.

Question 7

In a maximization problem, when one or more of the solution variables and the profit can be made infinitely large without violating any constraints, the linear program has

Accepted Answer

An unbounded solution means that the feasible region is not bounded, so the solution variables and the objective function can be increased infinitely without violating any constraints. This is the case when there are no constraints limiting the values that the solution variables can take. In such a scenario, the linear programming problem does not have an optimal solution.

Question 8

When using Solver to find a solution for an LP problem, both the left-hand side and the right-hand side of your constraints must be a formula calculated using the cells containing the decision variables.

Accepted Answer

In Solver for LP problems, the left-hand side (LHS) of the constraints often involves formulas using the decision variables, but the right-hand side (RHS) can be constants or directly entered values, not necessarily formulas.

Question 9

Unlike a maximization problem, a two-variable minimization problem may not be solved graphically.

Accepted Answer

False. A two-variable minimization problem can be solved graphically using level curves or contour plots. The point where the contour lines are closest together is the minimum point.

Question 10

A widely used mathematical programming technique designed to help managers and decision making relative to resource allocation is called

Accepted Answer

Linear programming is a popular mathematical programming technique used by managers to allocate resources efficiently by optimizing a linear objective function subject to linear constraints. It helps in decision making by maximizing profits, minimizing costs, and allocating resources optimally.

Question 11

If the isoprofit line is not parallel to a constraint, then the solution must be unique.

Accepted Answer

If the isoprofit line is not parallel to a constraint, it means that it intersects the constraint at a unique point. Therefore, the optimal solution is unique.

Question 12

Which of the following is not a property of linear programs?

Accepted Answer

Linear programs can have one or multiple feasible regions, but they cannot have less than one. Therefore, option B is not a property of linear programs.

Question 13

A feasible solution to a linear programming problem

Accepted Answer

A feasible solution to a linear programming problem must satisfy all of the problem's constraints simultaneously, including any equality or inequality constraints as well as non-negativity constraints. It does not necessarily have to be a corner point or give the maximum profit; those characteristics pertain to optimal solutions under certain conditions, not to feasible solutions in general.

Question 14

In a minimization problem, the isocost line slides down and to the left through a feasible region to reflect decreasing costs.

Accepted Answer

In a minimization problem, the objective is to minimize costs while satisfying constraints. As costs decrease, the isocost line shifts down and to the left to represent the reduced expenditure needed to achieve the same level of output. Therefore, the statement is true.

Question 15

When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and

Accepted Answer

The optimal solution in a maximization linear programming problem is located at one of the corner points of the feasible region. This can be found by calculating the objective function (in this case, the profit) at each of the corner points and choosing the one with the highest value.

Question 16

The corner point solution method

Accepted Answer

The corner point solution method requires that the profit from all corners (or vertices) of the feasible region be compared to find the optimum solution. This method may yield different results from the isoprofit line solution method, which involves finding the optimal solution by analyzing the intersection of an isoprofit line with the feasible region. However, the corner point solution method can provide one, and only one, optimum solution if the objective function is linear and the feasible region is non-empty and bounded. Therefore, statement A may not always be true. Statement D is incorrect because not all corners are created by all constraints. Some corners may be created by only a subset of the constraints.

Question 17

Infeasibility in a linear programming problem occurs when

Accepted Answer

Infeasibility occurs when there is no solution that satisfies all the constraints given. This means that the constraints are conflicting, and it is impossible to find a feasible solution.

Question 18

The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n)________ of the feasible region.

Accepted Answer

The optimal solution of a linear programming problem lies at a corner point or extreme point of the feasible region, according to the fundamental theorem of linear programming. This is because the objective function, which is linear, will reach its maximum or minimum value at the boundary of the feasible region, specifically at one of its vertices or corner points.

Question 19

Sensitivity analysis enables us to look at the effects of changing the coefficients in the objective function, one at a time.

Accepted Answer

Sensitivity analysis allows us to examine how changes in the coefficients of the objective function impact the optimal solution, one at a time.

Question 20

Constraints do not need to be entered one at a time when using Solver.

Accepted Answer

Solver in Excel allows users to enter multiple constraints at once, facilitating the process of setting up complex optimization problems.

Quiz 7: Linear Programming Models: Graphical and Computer Methods