ECON 3300 Exam Review Ch. 4 Quizzes
A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit?
$380
The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B, which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds) 1 20 24 30 2 30 10 50 3 0 30 20 4 24 15 60 5 10 20 40 The constraint for ingredient 3 is:
.3B ≥ 20
Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York Stock Exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock 2". The constraint for this requirement can be written as:
.4x2 - .6x7 - .6x8 ≤ 0.
Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1.
.65x11 - .35x21 ≤ 0
Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil-base and water-base paint. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil-base paint, and y represents the gallons of water-base paint, which constraint is correctly represents the constraint on ingredient A?
.9x + .3y ≤ 10,000
The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50. Which of the following is not a feasible production combination?
0L and 1200V
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. An appropriate part of the model would be:
15X1 + 47.25X2 + 110 X3 ≤ 50,000.
The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50. What is the constraint for salt?
2L + 3V ≤ 4800
Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. What is an appropriate constraint for this fast food vignette?
2N + 4B + 4Q + 3E ≤ 400
Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. How many decision variables are in the LP formulation?
4
Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) A portion of the variable cells section of the sensitivity report in Excel appears in the table below. How many potential customers will be reached by the optimal advertising campaign? Final Reduced Objective Cell Name Value Cost Coefficient $C$2 Newspaper 0 -1000 5000 $D$2 Radio 13.76 0 3000 $E$2 Twitter 0 -800 700 $F$2 Facebook 4 0 200
42,080
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulated as a linear programming constraint?
47.25X2 ≤ 10,000 X2 + X3 ≤ 350
The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) Which of these is an appropriate constraint for this scenario?
500N + 250R + 125T + 15F ≤ 3,500
Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Leghorn Cochin Buff Orpington Eggs/week 5 2 4.5 Plumage 3 9 6 Temperament 2 8 5 Fertilizer 3 2 4 Appetite 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. The poultry farmer would like to generate 80 ounces of fertilizer per week while feeding a maximum of 160 ounces of layer pellets each week. Which of these constraints is correct?
5L + 4C + 8B ≤ 160
Balanced transportation problems have which of the following type of constraints?
=
Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Leghorn Cochin Buff Orpington Eggs/week 5 2 4.5 Plumage 3 9 6 Temperament 2 8 5 Fertilizer 3 2 4 Appetite 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. When he runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He can picture the sad little faces of his children when he tells them that there will be no variety of birds gracing their front lawn this summer. Help him avoid the embarrassment by selecting a constraint that will ensure that there is some variety in his flock.
C + B ≥ 5
Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) What is the proper interpretation of the shadow price for Facebook? Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$9 Facebook 4 20 4 229.3333333 4
Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 233.
The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) Which of these statements about the sensitivity report for the constraints is best? Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$5 Budget 3500 12 3500 2560 3440
For every $1 increase in the budget, the ad campaign can reach twelve more customers.
Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) How should the entry for the Newspaper decision variable be interpreted? Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$2 Newspaper 0 -1000 5000 1000 1E+30
If the director were forced to purchase a newspaper advertisement, he would reach 1000 fewer customers than would be reached using the optimal advertising campaign.
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is:
MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3.
Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. What is an appropriate objective function for this fast food vignette?
Max Z = 2.75N + 4B + 2Q + 3E
Atwitter The college director of global activities was hopeful that the print ads in the school newspaper and 30 second spots on the campus radio station would spur some interest in the array of study tour and study abroad options he had secured. The communications director for the college had other ideas; she favored a social media campaign consisting of tweets and facebook postings. "This is the most ridiculous thing I ever heard of," he whined to the dean. The communications director's market research revealed the following: Medium Exposure Cost Newspaper 5,000 $500 Radio 3,000 $250 Twitter 700 $25 Facebook 200 $15 The advertising budget is $3500, but there is no requirement that all the money be spent. The newspaper has only four issues before the end of the semester, but the radio is a 24/7 operation and has two dozen 30 second slots available. Facebook postings must be alternated with the rest of the mindless drivel posted on the college page; thus there is space for only three postings before the end of the semester. Twitter is complicated by the 140 character requirement. The communications director feels she needs five tweets to convey a single message about tours and semesters abroad, so for one message, the cost would be $25 for each of the five components of the single ad. Due to thumb fatigue, she feels that she has only 2800 characters left in her thumbs before the end of the semester. (A side note - During the intersession period, she plans to embark on a strict regimen of thumb yoga to prepare for the coming semester.) What is an appropriate objective function for this scenario?
Max Z = 5,000N + 3,000R + 700T + 200F
Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Leghorn Cochin Buff Orpington Eggs/week 5 2 4.5 Plumage 3 9 6 Temperament 2 8 5 Fertilizer 3 2 4 Appetite 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. Which of the following is an appropriate objective function?
Max Z = 5L + 2C + 4.5B
Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. Which of these is a decision variable for the LP formulation of this problem?
Nacholupa
Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. Which of the statements about this portion of the sensitivity report is best? Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $G$7 Cheese 400 0.25 400 16.66666667 233.3333333 $G$8 Meat 150 0.125 150 110 10
One additional pound of meat should be purchased if it can be acquired for $2 or less.
Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Leghorn Cochin Buff Orpington Eggs/week 5 2 4.5 Plumage 3 9 6 Temperament 2 8 5 Fertilizer 3 2 4 Appetite 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. When the poultry farmer runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He studies his sensitivity report (copied below) and decides to write a constraint that requires two Cochin chickens to be selected. If the current optimal mix of breeds results in 160 eggs per week, which of the following statements is best? Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease $B$1 Leghorn 32 0 5 1E+30 2.1875 $C$1 Cochin 0 -2 2 3 1E+30 $D$1 Buff Orpington 0 -3.5 4.5 3.5 1E+30
The new weekly egg output will be 153.
Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament. The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs. Bird Leghorn Cochin Buff Orpington Eggs/week 5 2 4.5 Plumage 3 9 6 Temperament 2 8 5 Fertilizer 3 2 4 Appetite 5 4 8 Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week. The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperament less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. Use this portion of the sensitivity report to evaluate the following statements: Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease $B$1 Leghorn 32 0 5 1E+30 2.1875 $C$1 Cochin 0 -2 2 3 1E+30 $D$1 Buff Orpington 0 -3.5 4.5 3.5 1E+30
The noise level around the farm should be over 60 decibels.
Taco Quatro Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. Which of these statements about the sensitivity report is best? Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $D$4 Burritaco 0 -0.125 4 0.125 1E+30 $C$4 Nacholupa 55 0 2.75 0.25 0.114
There are no Burritacos being made.
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct?
X1 ≤ 0.35(X1 + X2 + X3)
If Xab = the production of product a in period b, then to indicate that the limit on production of the company's 3 products in period 2 is 400, we write:
X12 + X22 + X32 ≤ 400.
In a multiperiod scheduling problem, the production constraint usually takes the form of:
beginning inventory - demand + production = ending inventory.
The type of linear program that compares services to indicate which one is less productive or inefficient is called:
data envelopment analysis.
A systematic approach to model formulation is to first:
define decision variables.
When systematically formulating a linear program, the first step is to:
identify the decision variables.
Let: rj = regular production quantity for period j, oj =overtime production quantity in period j, ij = inventory quantity in period j, and dj = demand quantity in period j. Correct formulation of the demand constraint for a multiperiod scheduling problem is:
rj + oj + i2 - i1 ≥ dj.
The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50. For the production combination of 800 bags of lime and 600 bags of vinegar, which of the three resources is (are) not completely used?
salt only
Compared to blending and product mix problems, transportation problems are unique because:
the solution values are always integers.
Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the supply constraint for component 1.
x11 + x12 ≤ 8000
Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons, respectively. Write the demand constraint for gasoline type 1.
x11 + x21 = 11000
