OR final exam

The shadow price of a nonbinding constraint is

0

Meaningful sensitivity report headings can be defined B

By carefully labeling rows and columns in the spreadsheet

Operations research got its start?

During World War 2

Which of the following describes MOLP problems correctly

Target values for different goals have to be identified by solving the problems with different objective function.

Almost all the network problems can be viewed as special cases as the

Transshipment problem

Which of the following properties of network flow models guarantee integer solutions?

Balance of flow rule constraints with integer coefficients and rhs values

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

Infeasible

Which of the following is not true about MOLP

The objective function minimizes the total weighted percentage deviation.

The reduced cost for a changing cell (decision variable) is..

The per unit profits minus the per unit costs for that variable

What weight would be assigned to a neutral deviational variable

0

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X1 = number of product 1 to make X2 = number of product 2 to make Max: 150X1 + 250X2 ST: 2X1 + 5X2 <= 200 3X1 + 7X2 <= 175 How much profit is earned by each unit of product 2 produced

250

The following linear programming problem has been written to plan the production of two products. The company wants to max. its profits. X1 = number of product 1 produced in each batch X2 = number of product 2 produced in each batch Max: 150 X1 + 250X2 ST: 2X2 + 5X2 <= 200 3X1 + 7X2 <= 175 How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

2750

How many constraints are there in a transportation problem which has 5 supply points and 4 demand points

9

For minimization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?

A lower bound

For maximization problems the optimal objective function to the LP relaxation provides what for the optimal objective function value of the ILP problem?

An upper bound

What does solvers default optimality tolerance factor of 5% accomplish?

Any ILP optimal objective function value is within 95% of the lP relaxation

How is the sub optimality factor of ILP set in solver? By...

Entering the tolerance in the solver options

Benefits of sensitivity analysis include all the following except

Fosters managerial acceptance of the optimal solution

A network flow problem that allows gains or losses along the arcs is called

Generalized network flow model

A zero in the allowable increase or allowable decrease for the objective function coefficient indicates that

In the absence of degeneracy, alternative optimal solutions exist

Which of the following special conditions in an LP model represent potential errors in the mathematical formulation

Infeasibility and unbounded solutions

If the shadow price for a resource is 1 and 150 units of the resource are added, what happens to the objective function value?

It is hard to say

Which is true about MOLP?

It uses the MINIMAX method The constraints are different from the ones used in GP models Target values need to be determined by solving the problem individually optimizing each objective

One approach to solving ILP problems is to ignore the integrity conditions and solve the problem with continuous decision variables. This is referred to as

LP Relaxation

Which of the following actions would expand the feasible region of an LP model

Loosening the constraints

A common objective in the product mix problem is

Maximizing profit

When a solution is degenerate the reduced costs for the changing cells

May not be unique

How many decision variables are needed in a transportation problem with n supply nodes and m demand nodes

N*m

If the shadow price for a resource is 0 and its allowable increase is infinity, what happens to the optimal solution if 150 units of the resource are added?

No change

A redundant constraint is one which

Plays no role in determining the feasible region of the problem

In the network created for an equipment replacement problem, a transshipment node represents?

Replacing the equipment with a brand new one

Consider modeling a warehouse with three in flow arcs and three outflow acrs. The warehouse node Is a transshipment node but has a capacity of 100. How would one modify the network model to avoid adding a side constraint that limits either the sum of in-flow or the sum of the out-flows to 100?

Separate the warehouse node into two nodes, connected by a single arc, with capacity of 100

To convert <= constraints into = constraints, the simplex method adds what type of variable to the constraint

Slack

To convert <= constraints to = constraints the simplex method adds what type of variable to the constraint?

Slack

A constraint whose RHS represents a target value of a goal in a problem is called a

Soft constraint

In generalized network flow problems

Solutions may not be integer values It can be difficult to tell if total supply meets total demand Flows along arcs may increase or decrease

Microsoft Excel, Quattro pro and lotus contain built-in optimizers called

Solvers

The constraints of an LP model define the

The constraints of an LP model define the

What is missing from the transportation problems compared to transshipment problems

Transshipment nodes

When the objective function can increase without ever contacting a constraint the LP model is said to be

Unbounded

A wedding caterer has several wine shops from which it can order champagne. The caterer needs 100 bottles of champagne on a particular weekend for 2 weddings. The relevant decision variable is defined as Xi = the number of bottles supplied by wine shop i Which set of constraints reflects wine shop 1's condition that it can supply either 40 bottles or 90 bottles?

X1 = 40Y11 + 90 Y12, Y11+Y12 <= 1

If a company selects either project 1 or project 2, then either project 3 or 4 must also be selected. Which of the following constraints enforce this condition.

X1+X2 <= 2(X3+X4)

If a company produces product 1, then it must produce at least 150 units of product 1. Which of the following constraints is the ILP constraint that enforce this condition.

X1-150Y1 >= 0

If a company selects project 1 then it must also select either project 2 or 3. Which of the following constraints enforce this condition

X1-X2-X3 <= 0

The optimal relaxed solution for an ILP has X1 = 2.7 and X2 = 1.8. If we branch on X2, what constraints must be added to the two resulting LP problems

X2<=1,X2>=2

How many constraints are there is a shortest path problem which has n nodes and m arcs.

n

For sure a problem from chapter 5 Equipment replacement Transshipment Generalized flow problem NO MOLP NO SIMPLEX

sure...