Omis 3202 Final Exam
Consistently using a structured, model based process to make decisions
Should produce good outcomes more frequently.
When the objective function can increase without ever contacting a constraint, the LP model is said to be
Unbounded
A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?
X1 + X2 + X3 + X4 = 1
The shadow price of a nonbinding constraint is
0
Variables are termed independent when they satisfy
The function value depends upon their values
A production company wants to ensure that if Product 1 is produced, production of Product 1 exceeds production of 50. Which of the following constraints enforce this condition?
X1<=M1Y1 ; X1>=50Yi
When a manager considers the effect of changes in an LP model's coefficients he/she is performing
a sensitivity analysis.
EVPI
expected value of perfect information
For a linear programming problem, assume that a given resource has not been fully used. We can conclude that the shadow price associated with that constraint
will have a value of zero.
Which of the following statements is true concerning either of the Allowable Increase and Allowable Decrease columns in the Sensitivity Report?
1. The values give the range over which an objective function coefficient can change without changing the optimal solution. 2. The values give the range over which a shadow price is accurate. 3. The values provide a means to recognize when alternate optimal solution exist.
The sensitivity analysis provides information about
1. the impact of adding simple upper or lower bounds on a decision variable. 2. the impact of a change in a resource level. 3. the impact of a change to an objective function coefficient.
The sensitivity analysis provides information about
1. the impact of adding simple upper or lower bounds on a decision variable. 2. the impact of a change to an objective function coefficient. 3. the impact of a change in a resource level.
Which of the following could not be a linear programming problem constraint?
1A + 2B /= 3
Product 1 (denoted by X1) requires 2 hours of processing time per kg. While product 2 (denoted by X2) requires 1 hour of processing time per kg, and for the coming month, 600 hrs of processing time are available. Which of the following equations correctly describes the above constraint?
2X1 + X2 <= 600
For maximization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem? Correct!
An upper bound.
A purely rational decision maker should
Consistently select the same alternative, regardless of how the problem is framed.
What is the goal in optimization?
Find the decision variable values that result in the best objective function and satisfy all constraints.
One approach to solving integer programming problems is to ignore the integrality conditions and solve the problem with continuous decision variables. This is referred to as
LP relaxation.
A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. Hours required by Operation. A B. Hours Cutting 3. 4 48 Welding 2 1 36 The decision variables are defined as Xi= the amount of product i produced Yi=1 if Xi>0 and 0 if Xi=0 What is the objective function for this problem?
Max: 17X1 + 21X2 - 60Y1 - 80Y2
Modeling techniques where the specifications of the relationships between dependent and independent variables unknown or ill-defined
Predictive Models
Solutions to which modeling technique indicates a course of action to the decision maker
Prescriptive models
Which of the following categories of modeling techniques includes optimization techniques?
Prescriptive models
In the following expression, which is (are) the dependent variable(s)? PROFIT = REVENUE - EXPENSES
Profit
Which of the following statements is false concerning either of the Allowable Increase and Allowable Decrease columns in the Sensitivity Report?
The values equate the decision variable profit to the cost of resources expended.
A company wants to select more than 2 projects from a set of 4 possible projects. Which of the following constraints ensures that more than 2 will be selected?
X1 + X2 + X3 + X4 >= 2
A company must invest in project 1 in order to invest in project 2. Which of the following constraints ensures that project 1 will be chosen if project 2 is invested in?
X1 - X2 >= 0
If a company produces Product 1, then it must produce at least 150 units of Product 1. Which of the following constraints enforces this condition? X1 stands for quantity of Product 1, and Y1=0,1 on whether or not to produce Product 1.
X1 − 150Y1 ≥ 0
Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component
X11 + X12 <= 8000
A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1's. It must produce more than 60 X2's for the X2 discount and 70 X3's for the X3 discount. Which of the following pair of constraints enforces the quantity discount relationship on X3? Note that we use Y3 , a binary variable with 1 denotes yes. This quantity discount is stepwise in the sense that the quantity below or equal to the threshold (certain limit) does not receive the discount while only that above the threshold receives the discount. X31 denotes the quantity of X3 without discount, and X32 denotes the quantity with discount. M3 is a big enough number.
X32 <= M3Y3 ; X31 >= 70Y3
When the allowable increase or allowable decrease for the objective function coefficient of one or more variables is zero it indicates (in the absence of degeneracy) that
alternate optimal solutions exist
A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is
an optimal solution
An LP problem with a feasible region will have
an optimal solution at some extreme point.
The objective function value for the ILP problem can never
be better than the optimal solution to its LP relaxation.
An integrality condition indicates that some (or all) of the
decision variables must be integer
What are the three common elements of an optimization problem?
decision variables, constraints, an objective.
If constraints are added to an LP model the feasible solution space will generally
decrease.
The setup cost incurred in preparing a machine to product a batch of product is an example of a
fixed charge.
Given an objective function value of 150 and a shadow price for resource 1 of 15, if 2 more units of resource 1 are added (assuming the allowable increase is greater than 10), what is the impact on the objective function value?
increase of 30
The decision with the smallest expected opportunity loss (EOL) will also have the
largest EMV
Decision variables
measure how much or how many items to produce, purchase, hire, etc.
The first step in solving a graphical linear programming model is to
plot the model constraints as equations on the graph and indicate the feasible solution area.
People who forgo a high expected value to avoid a disaster with a low probability are
risk averters.
A binding less than or equal to (≤) constraint in a maximization problem means
that all of the resource represented by the constraint is consumed in the solution.
The allowable decrease for a changing cell (decision variable) is
the amount by which objective function coefficient can decrease without changing the final optimal solution.
The allowable decrease for a constraint is
the amount by which the resource can decrease given the same shadow price.
The allowable increase for a constraint is
the amount by which the resource can increase given shadow price.
A binding greater than or equal to (≥) constraint in a minimization problem means that
the minimum requirement for the constraint has just been met.
Shadow Price
the rate of change of the optimal value as a result of a marginal change in the right-hand side of a constraint
