Deck 8: Linear Programming Applications

Question 1

The linear programming model of the production scheduling process is usually used when we have to schedule the production of a single product, requiring a mix of resources, over time.

Answer 1

False

Question 2

Linear programming variable names such as X₁₁, X₁₂, X₁₃, could possibly be used to represent production of a product (X_1j ) over several months.

Answer 2

True

Question 3

In a production scheduling problem, the inventory at the end of this month is set equal to the inventory at the end of last month + last month's production − sales this month.

Answer 3

False

Question 4

The linear programming model of the production mix problem only includes constraints of the less than or equal form.

Question 5

If a linear programming problem has alternate solutions, the order in which you enter the constraints may affect the particular solution found.

Question 6

Since the production mix linear program applications are a special situation, the number of decision variables is limited to two.

Question 7

Production scheduling is amenable to solution by LP because it is a problem that must be solved on a regular basis.

Question 8

An ingredient or blending problem is a special case of the more general problem known as diet and feed mix problems.

Question 9

The linear programming model of the production scheduling process can include the impact of hiring and layoffs, regular and overtime pay rates, and the desire to have a constant and stable production schedule over a several-month period.

Question 10

A media selection LP application describes a method in which media producers select customers.

Question 11

Another name for the transportation problem is the logistics problem.

Question 12

The linear programming approach to media selection problems is typically to either maximize the number of ads placed per week or to minimize advertising costs.

Question 13

Blending problems arise when one must decide which of two or more ingredients is to be chosen to produce a product.

Question 14

In formulating the media selection linear programming model, we are unable to take into account the effectiveness of a particular presentation (e.g., the fact that only 5 percent of the people exposed to a radio ad will respond as desired).

Question 15

Determining the mixture of ingredients for a most economical feed or diet combination would be described as a production mix type of linear program.

Question 16

A marketing research linear programming model can help a researcher structure the least expensive, statistically meaningful sample.

Question 17

The linear programming model of the production scheduling process is usually used when we have to schedule the production of multiple products, each of which requires a set of resources not required by the other products, over time.

Question 18

In general, linear programming is unable to solve complex labor planning as the objective function is usually not definable.

Question 19

The constraints in a transportation problem deal with requirements at each origin and capacities at each destination.

Question 20

Transporting goods from several origins to several destinations efficiently is called the transportation problem.

Question 21

Table 8-2
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 4 hours of assembly, 3 hours of finishing, and 1 hour of inspection. Each chair requires 3 hours of assembly, 2 hours of finishing, and 2 hours of inspection. The selling price per table is $140 while the selling price per chair is $90. Currently, each week there are 220 hours of assembly time available, 160 hours of finishing time, and 45 hours of inspection time. Assume that one hour of assembly time costs $5.00; one hour of finishing time costs $6.00; one hour of inspection time costs $4.50; and that whatever labor hours are not required for the table and chairs can be applied to another product. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-2, which describes a production problem, what would the objective function be?

A) Maximize T + C
B) Maximize 140T + 90C
C) Minimize 42.5T + 36C
D) Maximize 97.5T + 54C
E) Maximize 124.5T + 74.5C

Question 22

The following does not represent a factor a manager might typically consider when employing linear programming for a production scheduling:

A) labor capacity.
B) space limitations.
C) product demand.
D) risk assessment.
E) inventory costs.

Question 23

The linear programming truck loading model always results in a practical solution.

Question 24

Which of the following is considered a decision variable in the production mix problem of maximizing profit?

A) the amount of raw material to purchase for production
B) the number of product types to offer
C) the selling price of each product
D) the amount of each product to produce
E) None of the above

Question 25

In the linear programming transportation model, the coefficients of the objective function can represent either the cost or the profit from shipping goods along a particular route.

Question 26

The linear programming ingredient or blending problem model allows one to include not only the cost of the resource, but also the differences in composition.

Question 27

The linear programming transportation model allows us to solve problems where supply does not equal demand.

Question 28

Media selection problems are typically approached with LP by either

A) maximizing audience exposure or maximizing number of ads per time period.
B) maximizing the number of different media or minimizing advertising costs.
C) minimizing the number of different media or minimizing advertising costs.
D) maximizing audience exposure or minimizing advertising costs.
E) minimizing audience exposure or minimizing advertising costs.

Question 29

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

A) media selection.
B) marketing research.
C) portfolio assessment.
D) media budgeting.
E) All of the above

Question 30

Table 8-1
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-1, which describes a production problem, suppose it is decided that the number of hours used in the assembly process must be at least 90 percent of the number of hours used in the finishing department. How would this constraint be written?

A) 3T + 2C ≥ 162
B) 3T + 2C ≥ 0.9(2T + 2C)
C) 3T + 2C ≤ 162
D) 3T + 2C ≤ 0.9(2T + 2C)
E) None of the above

Question 31

Table 8-1
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-1, which describes a production problem, which of the following would be a necessary constraint in the problem?

A) T + C ≤ 40
B) T + C ≤ 200
C) T + C ≤ 180
D) 120T + 80C ≥ 1000
E) None of the above

Question 32

Table 8-1
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-1, which describes a production problem, suppose it is decided that the number of hours used in the assembly process must be at least 80 percent of the time available. How would this constraint be written?

A) 3T + 2C ≥ 160
B) 3T + 2C ≥ 200
C) 3T + 2C ≤ 200
D) 3T + 2C ≤ 160
E) None of the above

Question 33

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

A) the product mix problem.
B) the investment banker problem.
C) the Wall Street problem.
D) the portfolio selection problem.
E) None of the above

Question 34

Table 8-1
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-1, which describes a production problem, suppose it is decided that there must be 4 chairs produced for every table. How would this constraint be written?

A) T ≥ C
B) T ≤ C
C) 4T = C
D) T = 4C

Question 35

In production scheduling LP problems, inventory at the end of this month is set equal to ________.

A) inventory at the end of last month + this month's production − this month's sales
B) inventory at the beginning of last month + this month's production − this month's sales
C) inventory at the end of last month + last month's production − this month's sales
D) inventory at the beginning of last month + last month's production − last month's sales
E) inventory at the end of last month - this month's production + this month's sales

Question 36

Table 8-1
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-1, which describes a production problem, what would the objective function be?

A) Maximize T + C
B) Maximize 120T + 80C
C) Maximize 200T + 200 C
D) Minimize 6T + 5C
E) None of the above

Question 37

Table 8-1
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120 while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-1, which describes a production problem, which of the following would be a necessary constraint in the problem?

A) T + C ≥ 40
B) 3T + 2C ≤ 200
C) 2T + 2C ≤ 40
D) 120T + 80C ≥ 1000
E) None of the above

Question 38

Which of the following is considered a decision variable in the media selection problem of minimizing interview costs in surveying?

A) the number of people to survey in each market segment
B) the overall survey budget
C) the total number surveyed
D) the number of people to conduct interviews
E) None of the above

Question 39

Which of the following is considered a decision variable in the media selection problem of maximizing audience exposure?

A) the amount spent on each ad type
B) what types of ads to offer
C) the number of ads of each type
D) the overall advertising budget
E) None of the above

Question 40

Table 8-2
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 4 hours of assembly, 3 hours of finishing, and 1 hour of inspection. Each chair requires 3 hours of assembly, 2 hours of finishing, and 2 hours of inspection. The selling price per table is $140 while the selling price per chair is $90. Currently, each week there are 220 hours of assembly time available, 160 hours of finishing time, and 45 hours of inspection time. Assume that one hour of assembly time costs $5.00; one hour of finishing time costs $6.00; one hour of inspection time costs $4.50; and that whatever labor hours are not required for the table and chairs can be applied to another product. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-2, which describes a production problem, suppose it was decided that all the labor hour costs have to be covered through the sale of the tables and chairs, regardless of whether or not all the labor hours are actually used. How would the objective function be written?

A) Maximize 140T + 90C
B) Minimize 140T + 90C
C) Maximize 97.5T + 54C
D) Maximize T + C
E) Maximize 140T + 90C - 1100(T+C) - 960(T+C) - 202.5(T+C)

Question 41

Table 8-3
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
Referring to Table 8-3, which of the following constraints would be used?

A) 9T + 12B ≤ 12
B) 1T + 1B ≥ 10
C) 1T + 2B ≤ 12
D) All of the above
E) None of the above

Question 42

Suppose that the problem described in Table 8-2 is modified to specify that one-third of the tables produced must have 6 chairs, one-third must have 4 chairs, and one-third must have 2 chairs. How would this constraint be written?

A) C = 4T
B) C = 2T
C) C = 3T
D) C = 6T
E) None of the above

Question 43

Table 8-3
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
Referring to Table 8-3, suppose that this problem requires that you use all the varnish for the week. How would the linear programming representation change?

A) 1B + 1T ≤ 10 will become 1B + 1T ≤ 12.
B) 1B + 1T ≤ 10 will be replaced by 1B + 1T ≥ 10.
C) 1B + 1T ≤ 10 will become 1B + 1T = 10.
D) 2B + 1T ≤ 12 will become 2B + 1T = 12.
E) None of the above

Question 44

Table 8-5
Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways: CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 13 percent; and a money market mutual fund, which is expected to return 8 percent. She has decided that any or all of the $200,000 may be invested, but any part (or all) of it may be put in any of the 3 alternatives. Thus, she may have some money invested in all three alternatives. In formulating this as a linear programming problem, define the variables as follows:
According to Table 8-5, which describes an investment problem, which of the following would be the most appropriate constraint in the linear programming problem?

A) 0.06C + 0.13S + 0.08M ≤ 200000
B) C + S + M ≥ 200000
C) C + S + M ≤ 200000
D) C + S + M = 200000
E) None of the above

Question 45

Table 8-4
The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-4, which describes a labor planning problem and its solution, how many workers would actually be on duty during shift 1?

A) 12
B) 13
C) 0
D) 29
E) None of the above

Question 46

What is another name for blending problems?

A) diet problems
B) ingredient problems
C) feed mix problems
D) production mix problems
E) media selection problems

Question 47

Table 8-3
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
Referring to Table 8-3, which of the following constraints would be used?

A) Maximize 9T + 12B
B) 9T + 12B ≥ 12
C) 12T + 9B ≤ 10
D) 10T + 10B ≥ 10
E) None of the above

Question 48

Table 8-3
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
Referring to Table 8-3, the solution to the problem is

A) T = 10, B = 0.
B) T = 0, B = 10.
C) T = 0, B = 6.
D) T = 8, B = 2.
E) None of the above

Question 49

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

A) the product mix problem.
B) the investment banker problem.
C) the Wall Street problem.
D) the portfolio selection problem.
E) None of the above

Question 50

Linear programming is usually used by managers involved in portfolio selection to

A) maximize return on investment.
B) maximize investment limitations.
C) maximize risk.
D) minimize risk.
E) minimize expected return on investment.

Question 51

Table 8-5
Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways: CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 13 percent; and a money market mutual fund, which is expected to return 8 percent. She has decided that any or all of the $200,000 may be invested, but any part (or all) of it may be put in any of the 3 alternatives. Thus, she may have some money invested in all three alternatives. In formulating this as a linear programming problem, define the variables as follows:
According to Table 8-5, which describes an investment problem, suppose that Ivana has assigned the following risk factors to each investment instrument CDs (C): 1.2; stocks (S): 4.8; money market mutual fund (M): 3.2. If Ivana decides that she wants the risk factor for the whole investment to be less than 3.3, how should the necessary constraint be written?

A) 1.2C + 4.8S + 3.2M ≤ 3.3
B) C + S + M ≤ 3.3
C) 1.2C + 4.8S + 3.2M ≤ 3.3(C + S + M)
D) (1.2C + 4.8S + 3.2M)/3 ≤ 3.3
E) S = 0

Question 52

Table 8-4
The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Exhibit 8-4, which describes a labor planning problem and its solution, how many workers would be assigned to shift 4?

A) 1
B) 0
C) 14
D) 16
E) None of the above

Question 53

Table 8-2
A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 4 hours of assembly, 3 hours of finishing, and 1 hour of inspection. Each chair requires 3 hours of assembly, 2 hours of finishing, and 2 hours of inspection. The selling price per table is $140 while the selling price per chair is $90. Currently, each week there are 220 hours of assembly time available, 160 hours of finishing time, and 45 hours of inspection time. Assume that one hour of assembly time costs $5.00; one hour of finishing time costs $6.00; one hour of inspection time costs $4.50; and that whatever labor hours are not required for the table and chairs can be applied to another product. Linear programming is to be used to develop a production schedule. Define the variables as follows:
According to Table 8-2, which describes a production problem, suppose you realize that you can trade off assembly hours for finishing hours, but that the total number of finishing hours, including the trade-off hours, cannot exceed 240 hours. How would this constraint be written?

A) 7T + 5C ≤ 360
B) 3T + 2C ≤ 240
C) 4T + 3C ≤ 140
D) −T − C ≤ 80
E) None of the above

Question 54

Table 8-3
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
Referring to Table 8-3, which of the following constraints would be used?

A) 10T + 12B ≤ 12
B) 1T + 1B ≤ 10
C) 1T + 2B ≥ 12
D) All of the above
E) None of the above

Question 55

Table 8-4
The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-4, which describes a labor planning problem and its solution, how many workers would be assigned to shift 1?

A) 12
B) 13
C) 0
D) 2
E) None of the above

Question 56

Table 8-5
Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways: CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 13 percent; and a money market mutual fund, which is expected to return 8 percent. She has decided that any or all of the $200,000 may be invested, but any part (or all) of it may be put in any of the 3 alternatives. Thus, she may have some money invested in all three alternatives. In formulating this as a linear programming problem, define the variables as follows:
According to Table 8-5, which describes an investment problem, suppose that Ivana has decided that the amount invested in stocks cannot exceed one-fourth of the total amount invested. Which is the best way to write this constraint?

A) S ≤ 100,000/4
B) 0.13S ≤ 0.24C + 0.32M
C) -C + 4S - M ≤ 0
D) S ≤ (C + M) / 4
E) -C + 3S - M ≤ 0

Question 57

Table 8-4
The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-4, which describes a labor planning problem and its solution, how many workers would be assigned to shift 3?

A) 13
B) 14
C) 16
D) 0
E) None of the above

Question 58

When formulating transportation LP problems, constraints usually deal with the

A) number of items to be transported.
B) shipping cost associated with transporting goods.
C) distance goods are to be transported.
D) number of origins and destinations.
E) capacities of origins and requirements of destinations.

Question 59

Table 8-4
The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4).
According to Table 8-4, which describes a labor planning problem and its solution, how many workers would be assigned to shift 2?

A) 2
B) 0
C) 14
D) 15
E) None of the above

Question 60

Table 8-3
Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.
Referring to Table 8-3, if we were to frame this as a linear programming problem, the objective function would be:

A) Maximize 9B + 12T.
B) Maximize 9T + 12B.
C) Minimize 10T + 10B.
D) Maximize 12T + 10B.
E) None of the above

Question 61

What are the decision variables in the diet problem?

A) amount of each ingredient to use
B) number of ingredients to use
C) amount of each type of food to purchase
D) number of items of food to purchase
E) None of the above

Question 62

Dr. Malcomb Heizer wishes to invest his retirement fund of $2,000,000 so that his return on investment is maximized, but he also wishes to keep the risk level relatively low. He has decided to invest his money in any of three possible ways: CDs that pay a guaranteed 4 percent; stocks that have an expected return of 14 percent; and a money market mutual fund that is expected to return 18 percent. He has decided that the total $2,000,000 will be invested, but any part (or all) of it may be put in any of the three alternatives. Thus, he may have some money invested in all three alternatives. He has also decided to invest, at most, 30 percent of this in stocks and at least 20 percent of this in money market funds. Formulate this as a linear programming problem and carefully define all the decision variables.

Question 63

A computer start-up named Pear is considering entering the U.S. market with what they believe to be a smaller and faster computer than some of the existing products on the market. They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product. They want to collect a reasonable sample from across the U.S. representative of all age brackets. They have split the U.S. into 2 regions: East and West. They want to at least 65% of their sample to cover the East and no fewer than 25% of the West. They also have divided the age groups into 3 categories: 18-35, 36-69, and 70 and up. They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69. The costs per person surveyed is given in the table below: Assume that exactly 1,000 people are to be surveyed. The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements. Formulate this problem as a linear program.

Question 64

The shipping problem in LP is also called the

A) production mix problem.
B) freight train problem.
C) transportation problem.
D) land and sea problem.
E) None of the above

Question 65

Which of the following statements is false regarding the portfolio selection problem?

A) The typical objective is to maximize the expected return on investment
B) The contraints only pertain to risk
C) Typical applications include banks, mutual funds, investment services, and insurance companies
D) The problem typically includes both greater-than-or-equal-to and less-than-or-equal-to constraints
E) The problem can also factor in legal requirements

Question 66

When applying linear programming to diet problems, the objective function is usually designed to

A) maximize profits from blends of nutrients.
B) maximize ingredient blends.
C) minimize production losses.
D) maximize the number of products to be produced.
E) minimize the costs of nutrient blends.

Question 67

A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120, while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed six times the number of tables. How many tables and chairs should the furniture manufacturer produce to maximize profit?

Question 68

What is the objective in the truck loading problem?

A) minimize trucking distance
B) minimize the weight of the load shipped
C) maximize the value of the load shipped
D) minimize the cost of the load shipped
E) None of the above

Question 69

Swearingen and McDonald, a small furniture manufacturer, produces fine hardwood tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 12 hours of assembly, 20 hours of finishing, and 2 hours of inspection. Each chair requires 4 hours of assembly, 16 hours of finishing, and 3 hours of inspection. The profit per table is $150 while the profit per chair is $100. Currently, each week there are 300 hours of assembly time available, 220 hours of finishing time, and 30 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed 6 times the number of tables. Formulate this as a linear programming problem. Carefully define all decision variables. Find the solution.

Question 70

Which of the following statements is true regarding the labor planning problem?

A) It is typically a maximization problem.
B) Required labor hours translate into less-than-or-equal-to constraints.
C) The decision variables can include how many full and part-time workers to use.
D) The problem is only unique to banks.
E) None of the above

Question 71

What is the objective in the diet problem?

A) maximize nutrition
B) minimize number of ingredients
C) minimize calories
D) minimize cost
E) None of the above

Question 72

The following problem type is such a special case of linear programming that a special algorithm has been developed to solve it:

A) the production mix problem.
B) the diet problem.
C) the ingredient mix problem.
D) the transportation problem.
E) None of the above

Question 73

Ivana Miracle wishes to invest her full inheritance of $300,000, and her goal is to minimize her risk subject to an expected annual return of at least $30,000. She has decided to invest her money in any of three possible ways-CDs, which pay a guaranteed 6 percent; stocks, which have an expected return of 15 percent; and a money market mutual fund, which is expected to return 8 percent. Risk factors are 1.0 for the CDs, 3.6 for the stocks, and 1.8 for the money market fund. Formulate this as a linear program.

Question 74

A fast food restaurant uses full-time and part-time help to meet fluctuating demand during the day. The following table presents projected need for workers at different times of the day: There is a maximum of four full-time workers and the other workers are part-time workers. Each full-time worker is there from 9:00 until 5:00, while the part-time workers will work for 4 consecutive hours at a cost of $4.00 per hour. The cost of the full-time worker is $50 per day. The company wishes to minimize total cost while meeting the demands. Formulate this as a linear programming problem. Carefully define all decision variables.

Question 75

A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120, while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed six times the number of tables. Formulate this as a linear programming problem. Carefully define all decision variables.

Question 76

Cedar Point amusement park management is preparing the park's annual promotional plan for the coming season. Several advertising alternatives exist: newspaper, television, radio, and displays at recreational shows. The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium. Given an advertising budget of $250,000, how many placements should be made in each medium to maximize total audience exposure? Formulate this as a linear programming problem.

Question 77

When formulating transportation LP problems, the objective function usually deals with the

A) number of items to be transported.
B) choice of transportation mode (e.g., truck, airplane, railroad, etc.).
C) shipping cost or distances associated with transporting goods.
D) number of origins and destinations.
E) capacities of origins and requirements of destinations.

Question 78

A manufacturer of microcomputers produces four models: Portable, Student, Office, and Network. The profit per unit on each of these four models is $500, $350, $700, and $1000, respectively. The models require the labor and materials per unit shown below. Formulate this product mix problem using linear programming.

Question 79

A computer start-up named Pear is considering entering the U.S. market with what they believe to be a smaller and faster computer than some of the existing products on the market. They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product. They want to collect a reasonable sample from across the U.S. representative of all age brackets. They have split the U.S. into 2 regions: East and West. They want to at least 65% of their sample to cover the East and no fewer than 25% of the West. They also have divided the age groups into 3 categories: 18-35, 36-69, and 70 and up. They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69. The costs per person surveyed is given in the table below: Assume that exactly 1,000 people are to be surveyed. How many people should Pear Company survey from each age bracket within each region in order to minimize costs while meeting all requirements?

Question 80

First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return. The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, 25 percent Blue Chip Stock, and no more than 15 percent High Tech Stock. Formulate this portfolio selection problem using linear programming.