Quantitative Decision Making in Industry - Test 1

The terms 'stochastic' and 'deterministic' have the same meaning in quantitative analysis.

False

Uncontrollable inputs are the decision variables for a model.

False

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

False

A solution that satisfies all the constraints of a linear programming problem except the non-negativity constraints is

Infeasible

Identification and definition of a problem

Is the first step of decision making

In a feasible problem, an equal-to constraint cannot be nonbinding.

True

No matter what value it has, each objective function line is parallel to every other objective function line in a problem.

True

Problem solving encompasses both the identification of a problem and the action to resolve it.

True

Range of optimality is the range of values over which an objective function coefficient may vary without causing any change in the values of the decision variables in the optimal solution.

True

Sensitivity analysis in linear programming studies the stability of optimal solutions and the optimal objective value with respect to perturbations (small changes) in the input data.

True

Slack variables represent unused resources

True

The reduced cost for a positive decision variables is 0.

True

Decision Criteria

Are the ways to evaluate the choices faced by the decision maker

There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Identify the correct condition of break-even point if the variable x represents the number of units manufactured and sold.

45x = 50000 + 25x

A small firm builds galvanized swing sets. The investment in plant and equipment is $200,000. The variable cost per swing set is $500. The selling price of the swing set is $1,000. How many swing sets would have to be sold for the firm to make a profit of $50,000?

500

There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Identify the correct expression for total cost if the variable x represents the number of units manufactured and sold.

50000 + 25x

A small firm builds galvanized swing sets. The investment in plan and equipment s $200,000. The variable cost per swing set is $500. The selling price of the swing set is $1,000. How many swing sets would have to be sold for the firm to make a profit of $100,000.

600

The constraint 2x1 - x2 = 0 passes through the point (200,100).

False

The feasible solution is the best solution possible for a mathematical model.

False

In linear programming models, what is the final objective?

Maximization of minimization

Which of the following is a valid objective function for a linear programming problem (assuming x, y, and z are the decision variables)?

Min 4x + 3y + (2/3)z

To find the optimal solution to a linear programming problem using the graphical method

None of the alternatives are correct.

The maximization or minimization of the quantity is the

Objective of linear programming

Linear programming is a technique for the _______, subject to linear equality and linear inequality constraints.

Optimization of a linear objective function

The amount by which an objective function coefficient can change before a different set of values for the decision variables because optimal is the

Range of optimality

If a linear programming problem has only two decision variables then graphical solution methods can be used to perform _________ analysis on the objective function coefficients and the right hand side values for the constraint.

Sensitivity

_______ analysis in linear programming that helps in the study of stability for optimal solutions and the optimal objective value with respect to perturbations (small changes) in the input data.

Sensitivity

Decision alternatives

Should be identified before decision criteria are established.

Decision varaibles

Tell how much or how many of something to produce, invest, purchase, hire, etc.

If a constraint is redundant, it can be removed from the problem without affecting the feasible region.

True

If the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25.

True

In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.

True

In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved.

True

In quantitative analysis, the optimal solution is the mathematically best solution.

True

In the Excel formulation of a linear programming problem given above, Inspection and Packaging is a non-binding resource.

True

The constraint 5x1 - 2x2 <= 0 passes through the points (20,50).

True

The first step in the decision making process is to identify the problem.

True

The point (3,2) is feasible for the constraint 2x1 + 6x2 <= 30

True

The volume that results in total revenue equalling total cost is called the break-even point.

True

Variable cost portion of the total cost is depended on and varies with the production volume.

True

With Solver, you can find an optimal (maximum or minimum) value for a formula in one cell - called the objective cell - subject to constraints, or limits, on the values of other formula cells on a worksheet.

True

Which of the following statements is NOT true?

An infeasible solution violates all constraints.

There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Identify the correct expression for total profit/loss if the variable x represents the number of units manufactured and sold.

45x - 50000 - 25x

Setup cost at a chip. manufacturing facility is $3,000. Variable labor and material costs are $2 for each chip produced. Selling price for each chip is $5. What is the break-even number of chips to be manufactured?

1,000

A small firm builds galvanized swing sets. The investment in plant and equipment is $200,000. The variable cost per swing set is $500. The selling price of the swing set is $1,000. How many swing sets would have to be sold for the firm to break even?

400

There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is $25. The revenue per unit is projected to be $45. Identify the correct expression for total revenue if the variable x represents the number of units manufactured and sold.

45x

What is a mathematical model?

A representation of a problem where the objectives and constraints are described by mathematical expressions

Sensitivity analysis in linear programming studies the stability of optimal solutions with respect to perturbations in the data such as

All options are true

What does the standard form include when solving linear programming problems?

All options are true.

For linear programming problems, which of the following statements is NOT true?

An infeasible solution violates all constraints

The change in the value of the optimal solution per unit increase in the right-hand side fo the constraint (binding constraint) is called the ________ value of that resource.

Dual

In a multicriteria decision problem

Each of these choices are true.

The field of management science

Each of these choices are true.

A company seeks to maximize profit subject to limited availability of man-hours. Man-hours is a controllable input.

False

A feasible solution is one that satisfies at least one of the constraints in the problem.

False

A redundant constraint is a binding constraint.

False

Alternative optimal solutions occur when there is a feasible solution to the problem.

False

A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental (causing loss) to the objective.

True

All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or solution for the problem.

True

Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.

True

Desmos is an advanced graphing calculator implemented as a browser application and a mobil application.

True

Fixed cost portion of the total cost that does not depend on the production volume.

True

For any constraint, either its slack/surplus value must be zero or its dual prices must be zero.

True

A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 hours respectively. The employee hours available in a month are 1,500 for welding, 1,500 for assembly and 550 in painting. The contribution to profits are $100 for product X and $120 for product Y. What is the objective function Z to be maximized in this linear programming problem?

Z = 100X + 120Y