Stat Test 3 T/F

"Range of optimality" describes the impact of simultaneous changes in objective function values and right-hand-side values.

False

A change in the value of an objective function coefficient will always change the value of the optimal solution.

False

A feasible solution violates at least one of the constraints.

False

A linear programming model consists of only decision variables and constraints.

False

An extreme point is an optimal solution.

False

Because the management science model requires that parameters are known with certainty, sensitivity analysis is not used in practical, real-world applications of linear programming.

False

Each decision variable must appear in at least two constraints.

False

For a profit maximization problem, if the allowable increase for a coefficient in the objective function is infinite, then profits are unbounded.

False

If the objective function is parallel to a constraint, the constraint is infeasible.

False

In linear programming models , objective functions can only be maximized.

False

It takes two pounds of steel and three pounds of copper to make a particular product. If there are 100 pounds of steel and 100 pounds of cooper available, one constraint will be 2X1 + 3X2 <= 200.

False

Linear programming and integer linear programming both yield a great amount of sensitivity analysis.

False

Minimization linear programming models may not involve "<=" constraints.

False

Most computer linear programming packages readily accept constraints entered in fractional form, such as X1/X3.

False

Multiple optimal solutions occur when constraints are parallel to each other.

False

Sensitivity analysis can be used to determine the effect on the solution for changing several parameters at once.

False

Sensitivity ranges can be computed only for the right-hand sides of constraints.

False

A constraint is a linear relationship representing a restriction on decision making.

True

A parameter is a numerical value in the objective function and constraints.

True

All model parameters are assumed to be known with certainty.

True

The objective function always consists of either maximizing or minimizing some value.

True

An optimal solution must have no slack on at least one constraint.

True

Binding constraints are the constraints which intersect at the optimal solution point.

True

Graphical solutions to linear programming problems have an infinite number of possible objective function lines.

True

If two extreme points are optimal, then so is every point on the line segment connecting the two extreme points.

True

If we change the constraint quantity to a value outside the range of feasibility for that constraint quantity, the shadow price will change.

True

In the graphical approach, simultaneous equations may be used to solve for the optimal solution point.

True

Linear programming is a model consisting of linear relationships representing a firm's decisions given an objective and resource constraints.

True

Linear programming models are a subset of constrained optimization models that require the assumptions of continuity of the variables, certainty of the coefficients, additivity of terms, and proportionality of costs, profits, and the use of resources to the value of the decision variables.

True

Linear programming models exhibit linearity among all constraint relationships and the objective function.

True

Linear programming problems can be formulated both algebraically and on spreadsheets.

True

Nimble Automotive uses linear programming to produce a monthly production schedule for their manufacturing plant. Although the number of cars built is obviously an integer, the fractional part of a non-integer decision variable could be considered ?work in progress? at the end of the month.

True

The sensitivity range for an objective function coefficient (range of optimality) is the range of values over which the current optimal solution point (product mix) will remain optimal.

True

The shadow price for a positive decision variable is 0.

True

The term "sensitivity analysis" refers to testing how a problem solution reacts to changes in one or more of the model parameters.

True

The terms in the objective function or constraints are additive.

True

The values of decision variables are continuous or divisible.

True

When specifying linear constraints, the modeler must take into account the unit specification of the decision variables so that the units represented by the left side of the constraints are consistent with the units represented by the right side of the constraints.

True

When using the graphical method, only one of the four quadrants of an xy-axis needs to be drawn.

True

A linear programming model has a constraint that reflects a budget restriction of $100,000. The range of feasibility for this amount, reflected on the sensitivity report, is $85,000 to $325,000. Thus if the budget restriction is changed to $90,000, the optimal solution will not change.

False

A linear programming problem with all ?<=? functional constraints and nonnegative right hand side values will never be infeasible.

False

A minimization model of a linear program contains only surplus variables.

False

A non-binding constraint is always a redundant constraint.

False

A variable is a value that is usually a coefficient of a parameter in an equation.

False

An example of a decision variable in a linear programming problem is profit maximization.

False

Slack variables are only associated with maximization problems.

False

Surplus variables are only associated with minimization problems.

False

The complementary slackness principle states that either there is zero slack on a constraint or the reduced cost is zero.

False

The difference between a boundary point and an extreme point is the number of constraints satisfied.

False

The first step of the management science process is to define the problem.

False

The objective function coefficient for X1 is currently $18 and for X2 is $29, and the ranges of optimality for these coefficients are between $15 and $20 and between $25 and $35, respectively. If the objective function coefficients for X1 and X2 decline by $2 each, since both coefficients are still within their ranges of optimality, the optimal solution is guaranteed to remain the same.

False

The optimal solution for a graphical linear programming problem is the corner point that is the farthest from the origin.

False

The range of feasibility for a constraint quantity value is the range over which the optimal values of the decision variables do not change.

False

The sensitivity range for an objective function coefficient is the range of values over which the value of the objective does not change.

False

The simplex method is a graphical technique used to solve all management science problems.

False

The terms shadow price and reduced cost mean the same thing.

False

There is exactly one optimal solution point to a linear program.

False

Typically, finding a corner point for the feasible region involves solving a set of three simultaneous equations.

False

When graphical method is used, we do not keep the scale of the unit on the grid paper the same.

False

When the right-hand sides of two constraints are both increased by one unit, the value of the objective function will be adjusted by the sum of the constraints' prices.

False

One of the reasons we cannot use sensitivity analysis for an integer linear program is that the shadow prices do not produce linear effects. That is, although in a linear program the shadow price for a resource represents the marginal improvement for each added unit of that resource, in an integer linear program, we cannot assume that each added unit of a resource will produce the same marginal change.

True

Parameters are known, constant values that are usually coefficients of variables in equations.

True

Sensitivity analysis determines how a change in a parameter affects the optimal solution.

True

Slack means the allowable reduction of a requirement without changing the optimal solution.

True

The feasible solution area contains infinite solutions to the linear program.

True

The marginal value, a.k.a shadow price, of any scarce resource is the dollar amount one should be willing to pay for one additional unit of that scarce resource.

True

The objective function is a linear relationship reflecting the objective of an operation.

True

The parameters of a model are the numbers in the data cells of a spreadsheet.

True

The sensitivity range for a constraint quantity value (range of feasibility) is the range over which the shadow price is valid.

True

You are currently paying $12 per hour for labor, and labor costs are included in the calculation of the objective function coefficients of a maximization problem. The shadow price for labor printed on the sensitivity analysis report is $8. It would be economically beneficial to you if you could secure extra labor for $15 per hour.

True