Deck 14: Optimization Models

Question 1

The LP relaxation of an integer programming (IP)problem is the same model as the IP model except that some integer constraints are omitted.

Answer 1

False

Question 2

If all the supplies and demands for a transportation model are integers,then the optimal Solver solution may or may not have integer-valued shipments.

Answer 2

False

Question 3

The optimal solution to an LP problem was 3.69 and 1.21.If and were restricted to be integers,then 4 and 1 will be a feasible solution,but not necessarily an optimal solution to the IP problem.

Answer 3

False

Question 4

Multiple optimal solutions are quite common in linear programming models.

Question 5

The transportation model is a special case of the minimum cost network flow model (MCNFM).

Question 6

In blending problems,if a quality constraint involves a quotient,then the problem will be nonlinear.

Question 7

If an LP problem is not correctly formulated,Solver will automatically indicate that it is infeasible when trying to solve it.

Question 8

Solver may be unable to solve some integer programming problems,even when they have an optimal solution.

Question 9

In network models of transportation problems,arcs represent the routes for getting a product from one node to another.

Question 10

In a transportation problem,if it costs $4 per item to ship up to 200 items between cities,and $2 per item for each additional item,the proportionality assumption of LP is satisfied.

Question 11

Integer programming (IP)models are optimization models in which all of the variables must be integers.

Question 12

Transportation costs for a given route are nearly always linear and smooth,with the main cost differences occurring between routes.

Question 13

Many of the most successful applications of optimization in the real world have been in the areas of scheduling,blending,logistics,and aggregate planning.

Question 14

Logistics problems are problems of finding the least expensive way to transport products from their origin to their destination.

Question 15

In transportation problems,the three sets of input numbers that are required are capacities,demands,and flows.

Question 16

In transportation problems,shipments between supply points or between demand points are possible.

Question 17

Transshipment points are locations where goods neither originate nor end up,but goods are allowed to enter such points to be shipped out to their eventual destinations.

Question 18

In transportation problem,shipping costs are often nonlinear due to quantity discounts.

Question 19

If Solver fails to find an optimal solution to an integer programming problem,we might be able to find a near optimal solution by increasing the Integer Optimality setting.

Question 20

When we solve a linear programming problem with Solver,we cannot guarantee that the solution obtained is an optimal solution.

Question 21

A global optimal solution is not necessarily the best solution overall.

Question 22

Aggregate planning models are usually implemented through a rolling planning horizon.

Question 23

A local optimal solution is better than all nearby solutions,but a solution far away might be better than it.

Question 24

Workforce scheduling problems are often integer programming models,which means that they have

A)an integer objective function.
B)integer decision variables.
C)integer constraints.
D)integer output.

Question 25

A 0-1 variable,also called a binary variable,is a variable that must equal 0 or 1.

Question 26

Many organizations must determine how to schedule employees to provide adequate service.If we assume that an organization faces the same situation each week,this is referred to as

A)a static scheduling problem.
B)a dynamic scheduling problem.
C)a transportation scheduling problem.
D)all of these choices.

Question 27

You should always look at the Solver solution for signs of implausibility.This can often help you spot an error in your model.

Question 28

Which of the following does not represent a broad class of applications of linear programming models?

A)Blending models
B)Financial portfolio models
C)Logistics models
D)Forecasting models

Question 29

In aggregate planning models,the number of workers available influences the possible production levels.

Question 30

In a set-covering model,each member of a given set (set 1)must be "covered" by an acceptable member of another set (set 2).The objective of such problems is to minimize the number of elements in set 2 that are needed to cover all the elements in set 1.

Question 31

A common characteristic of integer programming models is that they

A)are easy to solve graphically.
B)produce the same answer and standard linear programming models.
C)often produce multiple optimal solutions.
D)have all of these choices in common.

Question 32

For some types of integer programming problems,their LP relaxation solutions are optimal.

Question 33

In an optimized network flow model (MCNFM),all the available capacity will be used.

Question 34

Two common applications of optimization in finance are investment strategy and pension fund management.

Question 35

A nonlinear programming problem (NLP)is an optimization problem in which the objective function and/or the constraints are not linear functions of the decision variables.

Question 36

Any integer programming problem involving 0-1 variables with only one constraint is called a knapsack problem.

Question 37

Many organizations must determine how to schedule employees to provide adequate service.If we assume that an organization faces the same situation each week,this is referred to as a(n)_____ scheduling problem.

A)static
B)dynamic
C)transportation
D)organization

Question 38

The flows in a general minimum cost network flow model (MCNFM)all have to be from "left to right"; that is,from supply points to demand points.

Question 39

In aggregate planning models,we can model backlogging of demand by allowing a month's inventory to be negative.

Question 40

When we solve a nonlinear programming problem (NLP),it is very possible that Solver will obtain a suboptimal solution.

Question 41

The flow balance constraint for each transshipment node,in a minimum cost network flow model,takes which form?

A)Net Outflow = Capacity
B)Net Outflow < Capacity
C)Net Inflow=0 (equivalent to Net Outflow=0)
D)Net Inflow ≥ Demand

Question 42

A problem that deals with the direct distribution of products from supply locations to demand locations is called a(n)_____ problem.

A)transportation
B)assignment
C)network
D)transshipment

Question 43

In a minimum cost network flow model,the flow balance constraint for each supply node takes which form?

A)Net Inflow = Demand
B)Net Inflow ≥ Demand
C)Net Outflow > Capacity
D)Net Outflow ≤ Capacity

Question 44

The constraints in a blending problem can be specified in a valid way and still lead to which of the following problems?

A)Unboundedness
B)Insensitivity
C)Nonlinearity
D)Sensitivity

Question 45

The decision variables in transportation problems are

A)profits.
B)costs.
C)flows.
D)capacities.

Question 46

Which of these statements are true of multiple optimal solutions?

A)All solutions have the same values for the decision variables.
B)All solutions have the same value for the objective function.
C)All solutions have the same shadow prices.
D)All of these statements are true.

Question 47

In a network representation of a transportation problem,the nodes generally represent

A)warehouses.
B)geographic locations.
C)flows.
D)capacities.

Question 48

Transportation and transshipment problems are both considered special cases of a class of linear programming problems called _____ problems.

A)minimum cost
B)minimum cost network flow
C)supply locations network
D)demand locations network

Question 49

In a transshipment problem,shipments

A)can occur between any two nodes (suppliers,demanders,and transshipment locations).
B)cannot occur between two supply locations.
C)cannot occur between two demand locations.
D)cannot occur between a transshipment location and a demand location.

Question 50

In a typical minimum cost network flow model,the nodes indicate

A)roads.
B)rail lines.
C)geographic locations.
D)rivers.

Question 51

If refers to the number of hours that employee works in week ,then to indicate that the number of working hours of four employees in week 3 should not exceed 160 hours,we must have a constraint of the form

A) .
B) .
C) .
D) .

Question 52

In formulating a transportation problem as linear programming model,which of the following statements is not correct?

A)There are two constraints for each supply location.
B)There is one constraint for each demand location.
C)The sum of decision variables out of a supply location is constrained by the supply at that location.
D)The sum of decision variables out of all supply locations to a specific demand location is constrained by the demand at that location.

Question 53

To specify that must be at most 75% of the blend of , ,and ,we must have a constraint of the form

A) .
B) .
C) .
D) .
E) .

Question 54

Which of the following statements are false?

A)Solver does not offer a sensitivity report for models with integer constraints.
B)Solver's sensitivity report is not suited for questions about multiple input changes.
C)Solver's sensitivity report is used primarily for questions about one-at-a time changes to input.
D)None of these statements are false.

Question 55

A typical transportation problem requires which of the following sets of input numbers?

A)Capacities,demands,and flows
B)Capacities,demands,and unit shipping costs
C)Supplies,demands,and flows
D)Supplies,demands,and arcs

Question 56

In a network representation of a transportation problem,the arcs generally represent

A)warehouses.
B)geographic locations.
C)flows.
D)capacities.

Question 57

Which of the following is not a required input for a typical transportation problem?

A)Capacities (or supplies)
B)Demands
C)Unit shipping (and possibly production)costs
D)Distance from origins to destinations

Question 58

Rounding the solution of a linear programming problem to the nearest integer values provides a(n):

A)integer solution that is optimal.
B)integer solution that may be neither feasible nor optimal.
C)feasible solution that is not necessarily optimal.
D)infeasible solution.

Question 59

Which of the following is a type of constraint often required in blending problems?

A)Integer constraint
B)Binary constraint
C)Quality constraint
D)Nonlinear constraint

Question 60

The objective in transportation problems is typically to

A)maximize profits.
B)maximize revenue.
C)minimize costs.
D)maximize feasibility.

Question 61

A knapsack problem is any integer program involving 0 - 1 variable with _____ constraints.

A)three
B)two
C)one
D)zero

Question 62

Which of the following is not an example of a fixed cost?

A)Cash withdrawal fee from a bank
B)Monthly rent payment
C)Management salary
D)Hourly labor costs

Question 63

The project manager is evaluating options to complete the project early so that the company can earn a bonus.He has determined that the project schedule can be compressed into a six-month schedule,with the same total number of worker-months.In that case,the staffing requirements are as shown below. Develop an optimal staffing plan for the project under the accelerated schedule.

Question 64

A minimum cost network flow model (MCNFM)has the following advantage relative to the special case of a simple transportation model.

A)A MCNFM does not require capacity restrictions on the arcs of the network.
B)The flows in a general MCNFM don't all necessarily have to be from supply locations to demand locations.
C)A MCNFM is generally easier to formulate and solve.
D)All of these choices are advantages.

Question 65

A company manufactures two products.If it charges price for product I,it can sell units of product I,where and .It costs $25 to produce a unit of product 1 and $72 to produce a unit of product 2.How many units of each product should the company produce,and what prices should it charge,to maximize its profit?

Question 66

A company blends silicon and nitrogen to produce two types of fertilizers.Fertilizer 1 must be at least 40% nitrogen and sells for $75 per pound.Fertilizer 2 must be at least 70% silicon and sells for $45 per pound.The company can purchase up to 9000 pounds of nitrogen at $16 per pound and up to 12,000 pounds of silicon at $12 per pound.Assuming that all fertilizer produced can be sold,determine how the company can maximize its profit.

Question 67

A total of 160 hours of labor are available each week at $15 per hour.Additional labor can be purchased at $25 per hour.Capital can be purchased in unlimited quantities at a cost of $45 per unit.If K units of capital and L units of labor are available during a week,then machines can be produced.Each machine sells for $270.How can the firm maximize its weekly profit?

Question 68

You have decided to enter the candy business.You are considering producing two types of candies: A and B,both of which consist solely of sugar,nuts,and chocolate.At present you have in stock 12,000 ounces of sugar,3000 ounces of nuts,and 3000 ounces of chocolate.The mixture used to make candy A must contain at least 10% nuts and 10% chocolate.The mixture used to make candy B must contain at least 20% nuts.Each ounce of candy A can be sold for $0.40 and each ounce of candy for $0.50.Determine how you can maximize your revenues from candy sales.

Question 69

You are given the following means,standard deviations,and correlations for the annual return on three stocks.The means are 0.12,0.15,and 0.20.The standard deviations are 0.20,0.30,and 0.40.The correlation between stocks 1 and 2 is 0.65,between stocks 1 and 3 is 0.75,and between stocks 2 and 3 is 0.41.You have $13,000 to invest and can invest no more than half of your money in any single stock.Determine the minimum variance portfolio that yields an expected annual return of at least 0.14.

Question 70

In all optimization models,the objective cell has to be a function of the decision variable cells.It is perfectly consistent with this requirement to have the _____ be one of the _____.

A)range name,optimization models
B)input range,output cells
C)decision variable cell,objective cells
D)objective cell,decision variable cells

Question 71

During the next four quarters,an automobile company must meet (on time)the following demands for cars: 4000 in quarter 1; 2000 in quarter 2; 5000 in quarter 3; 1000 in quarter 4.At the beginning of quarter 1,there are 300 autos in stock.The company has the capacity to produce at most 3000 cars per quarter.At the beginning of each quarter,the company can change production capacity.It costs $100 to increase quarterly production capacity by 1 unit.For example,it would cost $20,000 to increase capacity from 3000 to 3200.It also costs $60 per quarter to maintain each unit of production capacity (even if it is unused during the current quarter).The variable cost of producing a car is $2200.A holding cost of $160 per car is assessed against each quarter's ending inventory.It is required that at the end of quarter 4,plant capacity must be at least 4000 cars.Determine how to minimize the total cost incurred during the next 4 quarters.

Question 72

Laila,an Egyptian broker,is currently trying to maximize her profit in the bond market.Four bonds are available for purchase and sale at the bid and ask prices shown in the table below: Laila can buy up to 1000 units of each bond at the ask price or sell up to 1000 units of each bond at the bid price.During each of the next 3 years,the person who sells a bond will pay the owner of the bond the cash payments shown in the table below: Laila's goal is to maximize her revenue from selling bonds less her payment for buying bonds,subject to the constraint that after each year's payments are received,her current cash position (due only to cash payments from bonds and not purchases or sales of bonds)is nonnegative.Note that her current cash position can depend on past coupons and that cash accumulated at the end of each year earns 13% annual interest.Determine how to maximize net profit from buying and selling bonds,subject to the constraints previously described.Why do you think we limit the number of units of each bond that can be bought or sold?

Question 73

In aggregate planning models,which of the following statements are correct?

A)The number of workers available influences the possible production levels.
B)We allow the workforce level to be modified each month through the hiring and firing of workers.
C)We eventually allow demand to be backlogged; that is,demand need not be met on time.
D)All of these choices are correct.

Question 74

In a minimum cost network flow model,the flow balance constraint for each demand node takes which form?

A)Net Outflow > Capacity
B)Net Inflow ≥ Demand
C)Net Outflow ≤ Capacity

Question 75

In nonlinear models,which of the following statements are correct?

A)Only the objective function is not a linear function of the decision variables.
B)Only the constraints are not linear functions of the decision variables.
C)The objective function and/or the constraints are not linear functions of the decision variables.
D)All of these statements are correct.

Question 76

A manufacturer can sell product 1 at a profit of $2 per unit and product 2 at a profit of $6 per unit.Three units of raw material are needed to manufacture one unit of product 1,and 6 units of raw material are needed to manufacture unit of product 2.A total of 120 units of raw material are available.If any of product 1 is produced,a setup cost of $10 is incurred,and if any of product 2 is produced,a setup cost of $20 is incurred.Determine how to maximize the manufacturer's profit.

Question 77

An oil company controls two oil fields.Field 1 can produce up to 45 million barrels of oil per day,and Field 2 can produce up to 55 million barrels of oil per day.At Field 1,it costs $3 to extract and refine a barrel of oil; at Field 2,the cost is $2.The company sells oil to two countries: France and Japan.The shipping costs per barrel are shown below. Each day,France is willing to buy up to 45 million barrels (at $6 per barrel),and Japan is willing to buy up to 35 million barrels (at $6.50 per barrel).What is the maximum profit the company can make?

Question 78

A large accounting firm has three auditors.Each can work up to 180 hours during the next month,during which time three projects must be completed.Project 1 takes 140 hours,Project 2 takes 150 hours,and Project 3 takes 170 hours.The amount per hour that can be billed for assigning each auditor to each project is given in the table below: Determine how to maximize total billings during the next month by formulating the company's problem as a transportation model.

Question 79

Determine the optimal staffing plan for this project.

Question 80

Determine how to minimize the company's total cost during the next four quarters.