QA 305 Exam 2

What are the four special cases and difficulties that arise at times when using the graphical approach to solving LP problems?

1. Infeasibility 2. Unboundedness 3. Redundancy 4. alternate optimal solutions

If a transportation problem has four origins and five destinations, the LP will have how many variables and constraints?

20 variables and 9 constraints

A company is considering opening one new production facility, and three locations are being considered. For this facility location problem, how many transportation models must be developed and solved

3

What is a binding constraint?

A constraint that has zero slack or surplus for the optimal solution

What is a non binding constraint?

A constraint with positive slack or surplus for the optimal solution

An assignment problem may be viewed as a transportation problem with

All supplies and demands equal to 1

What is it called when the isoprofit or isocost line runs perfectly parallel to one of the problem's constraint.. in other words they have the same slope?

Alternate optimal solution

What assumes that the numbers in objective and constraints are known with certainty and do not change during the period being studied

Certainity

What would cause a change in the feasible region?

Changing the right-hand side of a nonredunant constraint

What limit the degree to which we can pursue our objective?

Constraints

Which of the following methods is this: 1. Graph all constraints and find the feasible region 2. Find the corner points of the feasible region 3. Compute the profit (or cost) at each of the feasible corner points 4. select the corner point with the best value of the objective function found in step 3. This is the optimal solution

Corner point method

What LP is sometimes used to measure the efficiency of several similar operating units such as hospitals, or schools?

DEA- Data envelopment analysis

In LP, variables do not have to be integer valued.and may take on any fractional value. This assumption is called

Divisibility

What is an application of the transportation method to help a firm decide where to locate a new factory, warehouse, or other facility?

Facility location analysis

True or False: For a nonbinding constraint, obtaining additional units of that resource will result in higher profits?

False- it will not

What are the following steps? 1. Completely understand the managerial problem being faced 2. Identify the objective and the constraints 3. Define the decision variables 4. Use the decsion variables to write mathematical expressions for the objective function and the constraints

Formulating a Linear program

What is this sign : >=

Greater than or equal too

When would we remove or relax a constraint?

In solving a linear program, no feasible solution exists, to resolve this problem we might

What is this an example of: X1+2X2 <= 6 2X1+X2<=8 X1 >=7

Infeasibility

Which of the following methods is this: 1. Graph all constraints and find the feasibe region 2. Select a specific profit (or cost) line and graph it to find the slope 3. Move the objective function in the direction of increasing profit (or decreasing cost), while maintaining the slope 4. Find the values of the decision variables at this last point and compute the profit (or cost)

Isoprofit method

What type of LP address staffing needs over a specific time period?

Labor Planning

What does this sign represent <=?

Less than or equal too

What technique finds the maxiumum flow of any quantity or substance through a network

Maximal-flow

What is this an example of: Maximum number of cars that can flow through a highway system, the maximum amount of liquid that can flow through a series of pipes

Maximal-flow problem

Using LP to maximize audience exposure in an advertising campaign is an example of the type of LP application known as

Media selection

What are theses steps to: 1. Select any node in the network 2. Connect this node to othe nearest node that minimizes the total distance 3. Considering all of the nodes that are now connected, find and connect the nearest node that is not connected 4. Repeat the third step until all nodes are connected

Minimal-spanning tree technique

When applying LP to diet probelms the objective function is usually designed to

Minimize the costs of nutrient blends

What analysis means examining changes after the optimal solution has been reached?

Postoptimality analysis

What is it called when two or more products are usually produced using limited resources such as personnel, machines, raw materials, and so on..

Product Mix problem

Which problem use LP to decide how much of each product to make given a series of resource restrictions?

Product mix problems

What do these represent: 1. One objective function 2. One or more constraints 3. Alternative courses of action 4. Obejctive function and constraints are linear- proportionality and divisbility 5. Certaintiy 6. Divisibility 7. Nonnegative variables

Properties of linear programs

what constraint does not affect the feasible solution region

Redundant

What LP was designed to use differential pricing for seats so that additional revenue could be obtained

Revenue management

What is considered the final nore or destination in a network?

Sink

What equals the amount of resource available - amount of resource used

Slack

What is an origin or supply location in a transportation problem? Also the origin or beginning node in a maximal-flow network?

Source

which of the following does not represent a factor a manager might consider when employing LP for production scheduling? labor capacity, space limitations, product demand, risk assessment, and inventory costs

Space limitations

What equals the actual amount - minimum amount

Surplus

True or false the points on a network are referred to as nodes?

TRUE

When using a graphical solution procedure, the region bounded by the set of constraints is called what?

The feasible region

Which technique finds the shortest path through a network?

The shortest-route

A graphical method should only be used to solve an LP problem when?

There are only two variables

What does a transportation problem become if the items must go to a distrubution center before being shipped to the final destination?

Transhippment

T or F: Linear programming can be used to select effective media mixes, allocate fixed or limited budgets across media and maximize audience exposure

True

T or F: The diet problem is: also called the feed mix problem in agriculutre, a special case of the ingredient mix problem, a special case of the blending problem

True

True or False additivity means that the total of all activities equals the sum of the individual activities

True

True or False when a the profit in a maximization problem can be infinitely large, the problem is unbounded and is missing one or more constraints

True

True or False- In a transportation problem when you see Xij the i= the source and the j=the destination

True

True or False: In an LP problem, at least one corner point must be an optimal solution if an optimal solution exists

True

True or False: A destination is a demand location in a transportation problem

True

True or False: A feasible solution to an LP problem must satisfy all of the problems constraints.simultaneously

True

True or False: A network problem with the objective of minimizing the total distance or cost required to connect all nodes in the network is called minimal-spanning tree problem

True

True or False: An assignment problem is a special type of network problem in which costs are minimized while assigning people to jobs on a one-to-one basis?

True

True or False: For a binding constraint, obtaining additional units of that resource will result in higher profits?

True

True or False: In an assignement problem the person is the source and the project is the destination... ij

True

True or False: Media selection problems can be approached with the objective to maximize audience exposure or to minimize advertising costs?

True

True or False: Proportionality means that if production of 1 unit of a product uses 3 hours, production of 10 units would use 30 hours

True

True or False: Revenue management was first developed and used by American Airlines in the early 1900s

True

True or False: Slack is only associated with the <= constraints?

True

True or False: Surplus is only associated with the >= constraints?

True

True or False: The diet problem is one of the earliest applications of LP and was orginally used by hospitals to determine the most economical diet for patients?

True

True or False: The truck loading problem involves deciding which terms to load on a truck so as to maximize the value of a load shipped

True

True or False: in a minimization problem the shawdow price is negative of the dual price?

True

True or False: the lines connecting the nodes are called arcs

True

True or false divisibility assumes that solutions do not need to be in whole numbers but are divisible and may take any fractional value

True

True or false: In a maximization problem the shadow price is the same as the dual price?

True

true or false: The product mix problem is one of the most common LP problems

True

What is it called when the profit in a maximization problem can be infinitely large?

Unboundness

What is the assumption of nonnegative variables?

When working with LP you simply can't have -1 chair..

What is an example of integer programming?

When you have a fraction of a product. For example 1/3 of a chair

If a linear program is unbounded, the problem probably has not been formulated correctly. Which of the following would most likely cause this?

a constraint was inadvertently omitted

True or False: If a nonredundant constraint is removed from an LP problem, then the feasible region will get smaller

false: the feasible region will get larger

What is the typical transportation problem concerned with finding?

least cost way to distribute goods from sources

If the feasible region gets larger due to a change in one of the constraints, the optimal value of the objective function

must increase or remain the same for a maximization problem

Four cranes are being assigned to five construction jobs. One of the jobs will be delayed until one of the cranes becomes available after finishing the first specialized software to find a solution to this provelm

one dummy crane must be used in the model

An LP problem has a bounded feasible region. If this problem has an equality (=) constraint, then

the feasible region must consist of line segment

When alernate optimal solutions exist in an LP problem, then

the objective function will be parallel to one of the constraints

The selection of specific investments from among a wide variety of alternatives is the type of LP problem known as

the protfolio selection problem

True or False: A shadow price is the change in the objective function value that results from a one-unit increase in a right-hand side of a constraint

true

True or False: The dual price for a constraint is the improvement in the objective function value that results from a one-unit increase in the right-hand side of the constraint

true

When do blending problems arise?

when a decision must be made regarding the blending of two or more resources to produce one or more products