Deck 2: Linear programming: Basic Concepts

Question 1

A feasible solution is one that satisfies all the constraints of a linear programming problem simultaneously

Answer 1

True

Question 2

When formulating a linear programming problem on a spreadsheet,the Excel equation for each output cell can typically be expressed as a SUMPRODUCT function

Answer 2

True

Question 3

One of the great strengths of spreadsheets is their flexibility for dealing with a wide variety of problems

Answer 3

True

Question 4

All linear programming models have an objective function and at least two constraints

Question 5

An example of a decision variable in a linear programming problem is profit maximization

Question 6

Linear programming allows a manager to find the best mix of activities to pursue and at what levels

Question 7

When formulating a linear programming problem on a spreadsheet,the data cells will show the optimal solution

Question 8

A circle would be an example of a feasible region for a linear programming problem

Question 9

Linear programming problems can be formulated both algebraically and on spreadsheets

Question 10

Constraints limit the alternatives available to a decision-maker

Question 11

Linear programming problems may have multiple goals or objectives specified

Question 12

The feasible region only contains points that satisfy all constraints

Question 13

The line forming the boundary of what is permitted by a constraint is referred to as a parameter

Question 14

The origin satisfies any constraint with a ≥ sign and a positive right-hand side

Question 15

Since all linear programming models must contain nonnegativity constraints,Solver will automatically include them and it is not necessary to add them to a formulation

Question 16

The best feasible solution is called the optimal solution

Question 17

An infeasible solution violates all of the constraints of the problem

Question 18

When formulating a linear programming problem on a spreadsheet,objective cells will show the levels of activities for the decisions being made

Question 19

Linear programming problems always involve either maximizing or minimizing an objective function

Question 20

The parameters of a model are the numbers in the data cells of a spreadsheet

Question 21

A linear programming problem can have multiple optimal solutions

Question 22

The value of the objective function decreases as the objective function line is moved away from the origin

Question 23

When solving linear programming problems graphically,there are an infinite number of possible objective function lines

Question 24

Where are the data cells located?

A)B2:C2
B)B2:C2,B5:C7,and F5:F7
C)B10:C10
D)F10
E)None of the above

Question 25

When formulating a linear programming problem on a spreadsheet,which of the following is true?

A)Parameters are called data cells
B)Decision variables are called changing cells
C)Nonnegativity constraints must be included
D)The objective function is called the objective cell
E)All of the above

Question 26

A maximization problem can generally be characterized by having all ≥ constraints

Question 27

Linear programming models can have either ≤ or ≥ inequality constraints but not both in the same problem

Question 28

When solving a minimization problem graphically,it is generally the goal to move the objective function line out,away from the origin,as far as possible

Question 29

If a single optimal solution exists while using the graphical method to solve a linear programming problem,it will exist at a corner point

Question 30

The graphical method can handle problems that involve any number of decision variables

Question 31

For a graph where the horizontal axis represents the variable x and the vertical axis represents the variable y,the slope of a line is the change in y when x is increased by 1

Question 32

In linear programming,solutions that satisfy all of the constraints simultaneously are referred to as:

A)optimal
B)feasible
C)nonnegative
D)targeted
E)All of the above

Question 33

The equation 3xy = 9 is linear

Question 34

A manager should know the following things about linear programming

A)What it is
B)When it should be used
C)When it should not be used
D)How to interpret the results of a study
E)All of the above

Question 35

The equation 5x + 7y = 10 is linear

Question 36

Which of the following is not a component of a linear programming model?

A)Constraints
B)Decision variables
C)Parameters
D)An objective
E)A spreadsheet

Question 37

An objective function represents a family of parallel lines

Question 38

All constraints in a linear programming problem are either ≤ or ≥ inequalities

Question 39

When solving a maximization problem graphically,it is generally the goal to move the objective function line out,away from the origin,as far as possible

Question 40

A feasible point on the optimal objective function line is an optimal solution

Question 41

What is the constraint for Dominican beans?

A)12A + 8B ≤ 4,800
B)8A + 12B ≤ 4,800
C)4A + 8B ≤ 3,200
D)8A + 4B ≤ 3,200
E)4A + 8B ≤ 4,800

Question 42

What is the optimal solution for the following problem?

A)(x,y)= (0,0)
B)(x,y)= (0,3)
C)(x,y)= (0,5)
D)(x,y)= (1,2 5)
E)(x,y)= (6,0)

Question 43

Solving linear programming problems graphically,

A)is possible with any number of decision variables
B)provides geometric intuition about what linear programming is trying to achieve
C)will always result in an optimal solution
D)All of the above
E)None of the above

Question 44

Which of the following constitutes a simultaneous solution to the following 2 equations?

A)(x₁,x₂ )= (1,1 5)
B)(x₁,x₂ )= (0 5,2)
C)(x₁,x₂ )= (0,3)
D)(x₁,x₂ )= (2,0)
E)(x₁,x₂ )= (0,0)

Question 45

Which of the following is not a feasible solution?

A)(A,B)= (0,0)
B)(A,B)= (0,400)
C)(A,B)= (200,300)
D)(A,B)= (400,0)
E)(A,B)= (400,400)

Question 46

What is the optimal solution for the following problem?

A)(x,y)= (2,0)
B)(x,y)= (0,3)
C)(x,y)= (0,0)
D)(x,y)= (1,5)
E)None of the above

Question 47

Given the following 2 constraints,which solution is a feasible solution for a maximization problem?

A)(x₁,x₂ )= (1,5)
B)(x₁,x₂ )= (5,1)
C)(x₁,x₂ )= (4,4)
D)(x₁,x₂ )= (2,1)
E)(x₁,x₂ )= (2,6)

Question 48

What is the constraint for Colombian beans?

A)A + 2B ≤ 4,800
B)12A + 8B ≤ 4,800
C)2A + B ≤ 4,800
D)8A + 12B ≤ 4,800
E)4A + 8B ≤ 4,800

Question 49

After the data is collected the next step to formulating a linear programming model is to:

A)identify the decision variables
B)identify the objective function
C)identify the constraints
D)specify the parameters of the problem
E)None of the above

Question 50

When using the graphical method,the region that satisfies all of the constraints of a linear programming problem is called the:

A)optimum solution space
B)region of optimality
C)profit maximization space
D)feasible region
E)region of nonnegativity

Question 51

Where are the output cells located?

A)B2:C2
B)B2:C2,B5:C7,and F5:F7
C)B10:C10
D)F10
E)None of the above

Question 52

Which of the following constitutes a simultaneous solution to the following 2 equations?

A)(x₁,x₂ )= (2,0 5)
B)(x₁,x₂ )= (4,0 5)
C)(x₁,x₂ )= (2,1)
D)x₁ = x₂
E)x₂ = 2x₁

Question 53

What is the objective function?

A)P = A + 2B
B)P = 12A + 8B
C)P = 2A + B
D)P = 8A + 12B
E)P = 4A + 8B

Question 54

Given the following 2 constraints,which solution is a feasible solution for a minimization problem?

A)(x₁ ,x₂ )= (0 5,5)
B)(x₁ ,x₂ )= (0,4)
C)(x₁ ,x₂ )= (2,5)
D)(x₁ ,x₂ )= (1,2)
E)(x₁ ,x₂ )= (2,1)

Question 55

What is the weekly profit when producing the optimal amounts?

A)$0
B)$400
C)$700
D)$800
E)$900

Question 56

For the products A,B,C,and D,which of the following could be a linear programming objective function?

A)P = 1A + 2B +3C + 4D
B)P = 1A + 2BC +3D
C)P = 1A + 2AB +3ABC + 4ABCD
D)P = 1A + 2B/C +3D
E)All of the above

Question 57

Which of the following could not be a constraint for a linear programming problem?

A)1A + 2B ≤ 3
B)1A + 2B ≥ 3
C)1A + 2B = 3
D)1A + 2B
E)1A + 2B + 3C ≤ 3

Question 58

Where is the objective cell located?

A)B2:C2
B)B2:C2,B5:C7,and F5:F7
C)B10:C10
D)F10
E)None of the above

Question 59

Where are the changing cells located?

A)B2:C2
B)B2:C2,B5:C7,and F5:F7
C)B10:C10
D)F10
E)None of the above

Question 60

Which objective function has the same slope as this one: 4x + 2y = 20

A)2x +4y = 20
B)2x - 4y = 20
C)4x - 2y = 20
D)8x + 8y = 20
E)4x + 2y = 10

Question 61

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg.
What is the objective function?

A)P = 2L + 3D
B)P = 2L + 4D
C)P = 3L + 2D
D)P = 4L + 2D
E)P = 5L + 3D

Question 62

A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each.
What is the sugar constraint?

A)6B + 3C ≤ 4,800
B)1B + 1C ≤ 4,800
C)2B + 4C ≤ 4,800
D)4B + 2C ≤ 4,800
E)2B + 3C ≤ 4,800

Question 63

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case.
What is the daily profit when producing the optimal amounts?

A)$960
B)$1,560
C)$1,800
D)$1,900
E)$2,520

Question 64

The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers.
What is the sugar constraint?

A)2D + 3C ≤ 4,800
B)6D + 8C ≤ 4,800
C)1D + 2C ≤ 4,800
D)3D + 2C ≤ 4,800
E)4D + 5C ≤ 4,800

Question 65

An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each.
What is the time constraint?

A)1A + 1B ≤ 800
B)0 25A + 0 5B ≤ 800
C)0 5A + 0 25B ≤ 800
D)1A + 0 5B ≤ 800
E)0 25A + 1B ≤ 800

Question 66

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case.
What is the objective function?

A)P = 4R + 6S
B)P = 2R + 3S
C)P = 6R + 4S
D)P = 3R +2S
E)P = 5R + 5S

Question 67

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg.
Which of the following is not a feasible solution?

A)(L,D)= (0,0)
B)(L,D)= (0,120)
C)(L,D)= (90,75)
D)(L,D)= (135,0)
E)(L,D)= (135,120)

Question 68

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg.
What is the daily profit when producing the optimal amounts?

A)$0
B)$240
C)$420
D)$405
E)$505

Question 69

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case.
What is the time constraint?

A)2R +3S ≤ 720
B)2R + 5S ≤ 720
C)3R + 2S ≤ 720
D)3R + 5S ≤ 720
E)5R + 5S ≤ 720

Question 70

A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each.
Which of the following is not a feasible solution?

A)(B,C)= (0,0)
B)(B,C)= (0,1100)
C)(B,C)= (800,600)
D)(B,C)= (1100,0)
E)(B,C)= (0,1400)

Question 71

A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each.
What is the daily profit when producing the optimal amounts?

A)$580
B)$340
C)$220
D)$380
E)$420

Question 72

The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers.
Which of the following is not a feasible solution?

A)(D,C)= (0,0)
B)(D,C)= (0,1000)
C)(D,C)= (800,600)
D)(D,C)= (1600,0)
E)(D,C)= (0,1,200)

Question 73

A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each.
What is the objective function?

A)P = 0 3B + 0 2C
B)P =0 6B + 0 3C
C)P = 0 2B + 0 3C
D)P = 0 2B + 0 4C
E)P =0 1B + 0 1C

Question 74

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D). He can only get 675 gallons of malt extract per day for brewing and his brewing hours are limited to 8 hours per day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract. Each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg and profits for Dark beer are $2.00 per keg.
What is the time constraint?

A)2L +3D ≤ 480
B)2L + 4D ≤ 480
C)3L + 2D ≤ 480
D)4L + 2D ≤ 480
E)5L + 3D ≤ 480

Question 75

The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers.
What is the daily profit when producing the optimal amounts?

A)$800
B)$500
C)$640
D)$620
E)$600

Question 76

The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers.
What is the objective function?

A)P = 0 5D + 0 4C
B)P =0 2D + 0 3C
C)P = 0 4D + 0 5C
D)P = 0 1D + 0 2C
E)P =0 6D + 0 8C

Question 77

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R) and sassafras soda (S). There are at most 12 hours per day of production time and 1500 gallons per day of carbonated water available. A case of root beer requires 2 minutes of time and 5 gallons of water to produce, while a case of sassafras soda requires 3 minutes of time and 5 gallons of water. Profits for the root beer are $6.00 per case, and profits for the sassafras soda are $4.00 per case.
Which of the following is not a feasible solution?

A)(R,S)= (0,0)
B)(R,S)= (0,240)
C)(R,S)= (180,120)
D)(R,S)= (300,0)
E)(R,S)= (180,240)

Question 78

An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each.
Which of the following is not a feasible solution?

A)(A,B)= (0,0)
B)(A,B)= (0,1000)
C)(A,B)= (1800,700)
D)(A,B)= (2500,0)
E)(A,B)= (100,1600)

Question 79

An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each.
What is the weekly profit when producing the optimal amounts?

A)$10,000
B)$4,600
C)$2,500
D)$5,200
E)$6,400

Question 80

An electronics firm produces two models of pocket calculators: the A-100 (A) and the B-200 (B). Each model uses one circuit board, of which there are only 2,500 available for this week's production. In addition, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators. Each A-100 requires 15 minutes to produce while each B-200 requires 30 minutes to produce. The firm forecasts that it could sell a maximum of 4,000 of the A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each and profits for the B-200 are $4.00 each.
What is the objective function?

A)P = 4A + 1B
B)P = 0 25A +1B
C)P = 1A + 4B
D)P = 1A + 1B
E)P = 0 25A + 0 5B