AGEC 3413 Chapter

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84) For the production combination of 16 pumpkin, 125 chipotle-adobo, and 124 basement, which resource is not completely used up and how much is remaining?

1 ounce salt, 325 ounces herbs, and 768 ounces maize

36) A balanced transportation model should have ________ constraints.

= or "equal to"

86) What is the optimal product mix and resulting profit?

A profit of $235 is attainable if Artisanal Chips, Etc., produces 150 bags of pumpkin and 400 bags of basement flavored chips.

61) 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? A) $380 B) $400 C) $420 D) $440

A) $380

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. 76) An appropriate part of the model would be: A) 15X1 + 47.25X2 + 110 X3 ≤ 50,000. B) MAX 15X1 + 47.25X2 + 110X3. C) X1 + X2 +X3 ≤ 50,000. D) MAX 50(15)X1 + 50 (47.25)X2 + 50 (110)X3.

A) 15X1 + 47.25X2 + 110 X3 ≤ 50,000.

The owner of Artisanal Chips etc. produces three flavors of artisanal corn chips marketed at new college graduates — pumpkin (P), chipotle adobo (A) and basement (B). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 1,000 ounces of salt, 2,000 ounces of maize, and 1,200 ounces of herbs. A bag of pumpkin chips requires 2 ounces of salt, 6 ounces of maize, and 1.75 ounces of herbs to produce; while a bag of chipotle-adobo chips requires 6 ounces of salt, 6 ounces of maize, and 5 ounces of herbs. A bag of basement chips requires 1.75 ounces of salt, 3.5 ounces of maize, and 1.5 ounces of herbs. Profits for a bag of basement chips are $0.40, for chipotle-adobo chips is $0.60, and for a bag of pumpkin chips $0.50. 43) What is the constraint for salt? A) 2P + 6C + 1.75B ≤ 1000 B) 2P + 3C + 4B ≤ 1000 C) 3P + 6C + 3.5B ≤ 2000 D) 3P + 3C + 4B ≤ 2000

A) 2P + 6C + 1.75B ≤ 1000

53) Which of these is an appropriate constraint for this scenario? A) 5,000N + 3,000R + 700T + 200F ≤ 3,500 B) 500N + 250R + 125T + 15F ≤ 3,500 C) N + R + T + F ≥ 36 D) T ≤ 2,800

A) 5,000N + 3,000R + 700T + 200F ≤ 3,500

56) What is the proper interpretation of the shadow price for Facebook? Name FV SP R.H.S. AI AD Newspaper 4 20 4 229.333 4 A) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 233. B) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 229. C) If they spend $4, then can reach 20 customers. D) If they spend less than $20, they can reach 229.333 customers.

A) Every additional dollar spent on Facebook advertising gains 20 customers as long as the number of postings does not exceed 233.

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. 46) What is an appropriate objective function for this fast food vignette? A) Max Z = 2.75N + 4B + 2Q + 3E B) Min Z = 400C + 150M + 400B + 250T C) Min Z = 2.75N + 4B + 2Q + 3E D) Max Z = 400C + 150M + 400B + 250T

A) Max Z = 2.75N + 4B + 2Q + 3E

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.) 52) What is an appropriate objective function for this scenario? A) Max Z = 5,000N + 3,000R + 700T + 200F B) Max Z = 500N + 250R + 125T + 15F C) Min Z = 500N + 250R + 125T + 15F D) Min Z = 5,000N + 3,000R + 700T + 200F

A) 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 5 9 6 Temperament 5 8 5 Fertilizer 5 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. 62) Which of the following is an appropriate objective function? A) Max Z = 5L + 2C + 4.5B B) Max Z = 10L + 10C + 10B C) Min Z = 5L + 2C + 4.5B D) Min Z = 10L + 10C + 10B

A) Max Z = 5L + 2C + 4.5B

66) 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: Name FV RC OC. AI AD Leghorn 32 0 2 1E+30 2.1875 Cochin 0 -2 5 3 1E+30 Buff Opington 0 -3.5 4.5 3.5 1E+30 A) The noise level around the farm should be over 60 decibels. B) The fertilizer generated will be 160 ounces per week. C) Layer pellets will be consumed at the rate of 96 ounces per week. D) The plumage score will be less than 40.

A) The noise level around the farm should be over 60 decibels.

50) Which of these statements about the sensitivity report is best? NAME FV RC OC AI AD Burritaco 0 -0.125 4 0.125 1E+30 Nacholupa 55 0 2.75 0.25 0.114 A) There are no Burritacos being made. B) If the Nacholupa has a cost reduction of more than 0, none will be made. C) The company can make up to 1E + 30 Burritacos. D) The company can make an additional 0.25 Nacholupas if they want to with the leftover ingredients.

A) There are no Burritacos being made.

72) 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: A) rj + oj + i2 - i1 ≥ dj. B) rj + oj + i1 - i2 ≥ dj. C) rj + oj + i1 - i2 ≤ dj. D) rj - oj - i1 + i2 ≥ dj.

A) rj + oj + i2 - i1 ≥ dj.

45 records are produced by Jackson Enterprises at three different locations, 1, 2, and 3, and shipped to three sales centers named A, B and C. Company creative director Michael is unconcerned with efficiency, but operations manager Tito wishes to move the product as inexpensively as possible. The cost to transport one crate from each source to each destination is indicated in the table. as well as the demand at each sales center and the supply at each manufacturing facility. A B C Total Supply 1 $5 $6 $7 320 2 $6 $9 $8 420 3 $7 $4 $6 520 Total Demand 400 400 460 79) Which of these is an appropriate constraint for the problem? A) x1A + x1B +x1C = 320 B) x1A + x2A +x3A = 320 C) x3A + x3B +x3C = 460 D) x1B + x2B +x3B = 420

A) x1A + x1B +x1C = 320

B) $7120

The owner of Artisanal Chips etc. produces three flavors of artisanal corn chips marketed at new college graduates — pumpkin (P), chipotle adobo (A) and basement (B). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 1,000 ounces of salt, 2,000 ounces of maize, and 1,200 ounces of herbs. A bag of pumpkin chips requires 2 ounces of salt, 6 ounces of maize, and 1.75 ounces of herbs to produce; while a bag of chipotle-adobo chips requires 6 ounces of salt, 6 ounces of maize, and 5 ounces of herbs. A bag of basement chips requires 1.75 ounces of salt, 3.5 ounces of maize, and 1.5 ounces of herbs. Profits for a bag of basement chips are $0.40, for chipotle-adobo chips is $0.60, and for a bag of pumpkin chips $0.50. 44) Which of the following is not a feasible production combination? A) 128B and 128C B) 128C and 128P C) 128P and 128B D) 150P, 10C and 360B

B) 128C and 128P

63) 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? A) 3L + 2C + 4C ≤ 80 B) 5L + 4C + 8B ≤ 160 C) 5L + 4C + 8B ≥ 160 D) 5L + 4C + 8B ≥ 80

B) 5L + 4C + 8B ≤ 160

57) How should the entry for the Newspaper decision variable be interpreted? Name FV RC OC. AI AD Newspaper 0 -1000 5000 1000 1E+30 A) The director should lower the newspaper advertising expense by $1,000 to reach the objective of 5,000 customers contacted. B) 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. C) If the director increased newspaper advertisement by 1,000, he would spend $1000 less than with the current campaign. D) It is possible to reach an almost infinite fewer number (10 to the 30th power) of customers by newspaper than by any other method.

B) 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. 77) The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is: A) MAX .06X1 +.08X2 +.11X3. B) MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3. C) MAX 15X1 + 47.25X2 +.110X3. D) MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3.

B) MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3.

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. 47) Which of these is a decision variable for the LP formulation of this problem? A) cheese B) Nacholupa C) 400 D) $2.75

B) Nacholupa

51) Which of the statements about this portion of the sensitivity report is best? NAME FV RC OC AI AD Cheese 400 0.25 400 16.66667 233.3333 Meat 150 0.125 150 0.25 10 A) Cheese costs more than meat. B) One additional pound of meat should be purchased if it can be acquired for $2 or less. C) There is both cheese and meat left over if the optimal product mix is produced. D) The shadow price of cheese can rise to 16.8167 before the right hand side changes.

B) One additional pound of meat should be purchased if it can be acquired for $2 or less.

73) In a multiperiod scheduling problem, the production constraint usually takes the form of: A) beginning inventory + demand - production = ending inventory. B) beginning inventory - demand + production = ending inventory. C) beginning inventory - ending inventory + demand = production. D) beginning inventory + demand + production = ending inventory.

B) beginning inventory - demand + production = ending inventory.

74) The type of linear program that compares services to indicate which one is less productive or inefficient is called: A) product mix. B) data envelopment analysis. C) marketing. D) blending.

B) data envelopment analysis.

26) ________ types of linear programming problems often result in fractional relations between variables which must be eliminated.

Blending

40) 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: A) x2 ≥ .60. B) x2 ≥ .60 (x2 + x7 + x8). C) .4x2 - .6x7 - .6x8 ≤ 0. D) .4x2 - .6x7 - .6x8 ≥ 0.

C) .4x2 - .6x7 - .6x8 ≤ 0.

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. 48) What is an appropriate constraint for this fast food vignette? A) 250T + 400B + 150M + 400C B) 4C + 1M + 0B + 4T ≤ 4 C) 2N + 4B + 4Q + 3E ≤ 400 D) 2.75N + 4B + 2Q + 3E

C) 2N + 4B + 4Q + 3E ≤ 400

54) 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? Name FV RC OC Newspaper 0 -1000 5000 Radio 13.76 0 3000 Twitter 0 -800 700 Facebook 0 0 200 A) 17.76 B) 8,900 C) 42,080 D) cannot be determined from the sensitivity report

C) 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. 75) 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? A) X2 ≤ 10000 X2 + X3 ≤ 350 B) 10,000 X2 ≤ 350X2 + 350X3 C) 47.25X2 ≤ 10,000 X2 + X3 ≤ 350 D) 47.25X2 ≤ 10,000 47.25 X2 + 110X3 ≤ 350

C) 47.25X2 ≤ 10,000 X2 + X3 ≤ 350

59) Balanced transportation problems have which of the following type of constraints? A) ≥ B) ≤ C) = D) <

C) =

64) 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. A) 5L + 4C + 8B ≤ 160 B) 5L + 4C + 8B ≥ 160 C) C + B ≥ 5 D) L + C + B ≥ 5

C) C + B ≥ 5

78) The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? A) X1 ≤ 0.35 B) X1 = 0.35 (50000) C) X1 ≤ 0.35(X1 + X2 + X3) D) X1 = 0.35(X1 + X2 + X3)

C) X1 ≤ 0.35(X1 + X2 + X3)

58) 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: A) X32 ≤ 400. B) X21 + X22 + X23 ≤ 400. C) X12 + X22 + X32 ≤ 400. D) X12 + X22 + X32 ≥ 400.

C) X12 + X22 + X32 ≤ 400.

71) A systematic approach to model formulation is to first: A) construct the objective function. B) develop each constraint separately. C) define decision variables. D) determine the right hand side of each constraint.

C) define decision variables.

The owner of Artisanal Chips etc. produces three flavors of artisanal corn chips marketed at new college graduates — pumpkin (P), chipotle adobo (A) and basement (B). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 1,000 ounces of salt, 2,000 ounces of maize, and 1,200 ounces of herbs. A bag of pumpkin chips requires 2 ounces of salt, 6 ounces of maize, and 1.75 ounces of herbs to produce; while a bag of chipotle-adobo chips requires 6 ounces of salt, 6 ounces of maize, and 5 ounces of herbs. A bag of basement chips requires 1.75 ounces of salt, 3.5 ounces of maize, and 1.5 ounces of herbs. Profits for a bag of basement chips are $0.40, for chipotle-adobo chips is $0.60, and for a bag of pumpkin chips $0.50. 42) For the production combination of 100 bags of each flavor of chips, which of the three resources is (are) not completely used? A) maize only B) salt and maize only C) herbs maize and salt D) salt and herbs only

C) herbs maize and salt

39) When systematically formulating a linear program, the first step is to: A) construct the objective function. B) formulate the constraints. C) identify the decision variables. D) identify the parameter values.

C) identify the decision variables

67) 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. A) x21 + x22 ≤ 8000 B) x12 + x22 ≥ 8000 C) x11 + x12 ≤ 8000 D) x21 + x22 ≥ 8000

C) x11 + x12 ≤ 8000

41) 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 1, 20, 24, 30 Ingredient 2, 30, 10, 50 Ingredient 3, 0, 30, 20 Ingredient 4, 24, 15, 60 Ingredient 5, 10, 20, 40 The constraint for ingredient 3 is: A) .5A + .75B = 20. B) .3B = 20. C) .3B ≤ 20. D) .3B ≥ 20.

D) .3B ≥ 20.

69) 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. A) x11 + x12 (.35)(x11 + x21) B) x11 + .35(x11 + x12) C) -.65x11 + .35x21 ≤ 0 D) .65x11 - .35x21 ≤ 0

D) .65x11 - .35x21 ≤ 0

70) 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 correctly represents the constraint on ingredient A? A) .9A + .1B ≤ 10,000 B) .9x + .1y ≤ 10,000 C) .3x + .7y ≤ 10,000 D) .9x + .3y ≤ 10,000

D) .9x + .3y ≤ 10,000

The owner of Artisanal Chips etc. produces three flavors of artisanal corn chips marketed at new college graduates — pumpkin (P), chipotle adobo (A) and basement (B). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 1,000 ounces of salt, 2,000 ounces of maize, and 1,200 ounces of herbs. A bag of pumpkin chips requires 2 ounces of salt, 6 ounces of maize, and 1.75 ounces of herbs to produce; while a bag of chipotle-adobo chips requires 6 ounces of salt, 6 ounces of maize, and 5 ounces of herbs. A bag of basement chips requires 1.75 ounces of salt, 3.5 ounces of maize, and 1.5 ounces of herbs. Profits for a bag of basement chips are $0.40, for chipotle-adobo chips is $0.60, and for a bag of pumpkin chips $0.50. 45) Which of these answers is optimal? A) 120P, 100C, and 88B B) 130P, 88C and 100B C) 140P, 88C and 88B D) 150P and 400B

D) 150P and 400B

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. 49) How many decision variables are in the LP formulation? A) 1 B) 2 C) 3 D) 4

D) 4

55) Which of these statements about the sensitivity report for the constraints is best? Name FV SP R.H.S. AI AD Newspaper 3500 12 3500 2560 3440 A) Only $940 of the advertising budget is being spent on this campaign. B) The advertising campaign needs another $2,560 to reach the maximum number of customers. C) It is possible to reach enough customers by spending only $60. D) For every $1 increase in the budget, the ad campaign can reach twelve more customers.

D) For every $1 increase in the budget, the ad campaign can reach twelve more customers.

45 records are produced by Jackson Enterprises at three different locations, 1, 2, and 3, and shipped to three sales centers named A, B and C. Company creative director Michael is unconcerned with efficiency, but operations manager Tito wishes to move the product as inexpensively as possible. The cost to transport one crate from each source to each destination is indicated in the table. as well as the demand at each sales center and the supply at each manufacturing facility. 81) Suppose demand in sales center C drops to 400 units while demand in centers A and B both increase to 430. How does the problem formulation change? A) All of the constraints become less than or equal to constraints. B) Only the supply constraints become less than or equal to constraints. C) Only the demand constraints become less than or equal to constraints. D) The constraints do not change.

D) The constraints do not change.

65) 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? Name FV RC OC. AI AD Leghorn 32 0 2 1E+30 2.1875 Cochin 0 -2 5 3 1E+30 Buff Opington 0 -3.5 4.5 3.5 1E+30 A) The new weekly egg output will be 169. B) The new weekly egg output will be 162. C) The new weekly egg output will be 158. D) The new weekly egg output will be 153.

D) The new weekly egg output will be 153.

60) Compared to blending and product mix problems, transportation problems are unique because: A) they maximize profit. B) the constraints are all equality constraints with no "≤" or "≥" constraints. C) they contain fewer variables. D) the solution values are always integers.

D) the solution values are always integers.

68) 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. A) x21 + x22 = 11000 B) x12 + x22 = 11000 C) x11 + x21 ≤ 11000 D) x11 + x21 = 11000

D) x11 + x21 = 11000

10) The constraint x + y = z is written in standard form.

FALSE

11) In an unbalanced transportation model, supply does not equal demand, and supply constraints must have ≤ signs.

FALSE

12) Transportation problems can have solution values that are non-integer and must be rounded.

FALSE

15) A conservative approach to a balanced transportation model would be to make all constraints less-than-or-equal-to constraints.

FALSE

16) In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤).

FALSE

18) Fractional relationships among variables are considered standard form in a blending problem.

FALSE

19) Data envelopment analysis indicates which type of service unit makes the highest profit.

FALSE

2) Product mix problems cannot have greater-than-or-equal-to (≥) constraints.

FALSE

20) In a classic blending problem, revenue is maximized by subtracting cost from profit.

FALSE

22) Double-subscripted variables are required when there are two decision variables.

FALSE

24) A data envelopment analysis with an objective function value of 0.8 means the company is more efficient than its competitors since it expends only 80% of the effort to achieve the same results.

FALSE

3) When using a linear programming model to solve the diet problem, the objective is generally to maximize profit.

FALSE

4) When using a linear programming model to solve the diet problem, the objective is generally to maximize nutritional content.

FALSE

5) Diet problems usually maximize nutritional value.

FALSE

6) In most media selection decisions, the objective of the decision maker is to minimize cost.

FALSE

8) A linear programming model of a media selection problem is used to determine the relative value of each advertising media.

FALSE

85) The production combination of 180 bags of pumpkin and 100 bags of chipotle-adobo is not feasible because one resource is exceeded. Which resource is exceeded and how much more is needed to produce this combination?

Herbs only, 20 ounces are needed

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 (tablespoons) 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. The shop must produce at least 400 almond-filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. 88) What is the formulation for this problem?

MAX Z = $.20B + $.30C s.t. 6B + 3C ≤ 6600 1B + 1C ≤ 1400 2B + 4C ≤ 4800 C ≥ 400

MAX Z = 0. 5P + 0.6C + 0.4B s.t. 2P + 6C + 1.75B ≤ 1000 3P + 6C + 3.5B ≤ 2000 4P + 5C + 1.5B ≤ 1200

92) Formulate the appropriate LP model for this scenario.

Max Z = 5,000x1 + 3,000x2 + 700x3 + 200x4 Where x1 = Newspaper advertisements x2 = Radio advertisements x3 = Tweets x4 = Facebook postings

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.) 91) Formulate the appropriate objective function for this scenario.

Max Z = 5,000x1 + 3,000x2 + 700x3 + 200x4 Where x1 = Newspaper advertisements x2 = Radio advertisements x3 = Tweets x4 = Facebook postings

28) When the ________ command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed.

SUMPRODUCT

1) Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem.

TRUE

13) In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill).

TRUE

14) In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store).

TRUE

17) Blending problems usually require algebraic manipulation in order to write the LP in "standard form."

TRUE

21) Data envelopment analysis problems are usually maximization problems.

TRUE

23) A company can use regular time, overtime, and subcontracting in any amount over the one-year production planning horizon to meet forecasted demand. If they develop the plan using linear programming, they will have a total of 36 decision variables that govern the amount produced by these three methods.

TRUE

7) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure.

TRUE

9) In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

TRUE

82) Suppose demand in sales center C drops to 400 units. How does the problem formulation change and what is the optimal answer?

The supply constraints become "less than or equal to" constraints and the total amount shipped to location C must now equal 400. All of the demand constraints are "equal to" constraints to force the model to ship product. MIN Z = 5x1A + 6x1B + 7x1C + 6x2A + 9x2B + 8x2C + 7x3A + 4x3B + 6x3C s.t. x1A + x1B +x1C ≤ 320 x2A + x2B +x2C ≤ 420 x3A + x3B +x3C ≤ 520 x1A + x2A +x3A = 400 x1B + x2B +x3B = 400 x1C + x2C +x3C = 400 The solution has a total cost of $6,640 and sends 40 units from 1 to A, 280 units from 1 to C, 360 units from 2 to A, 400 units from 3 to B, and 120 units from 3 to C.

X12 + X22 + X32 ≤ 400

33) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the ________.

audience exposure

35) In a balanced transportation model, supply equals ________.

demand

29) Cranky Jerry's Day Care wants to minimize their food cost while meeting the minimum (and I mean bare minimum) guidelines for nutrition as set forth by the state. The best approach would be to follow the example in this chapter for a(n) ________ problem.

diet

25) Data envelopment analysis indicates the relative ________ of a service unit compared with others.

efficiency or productivity

flour = 600 ounces, almond paste = 400 TS

34) In a(n) ________ problem, maximization of audience exposure may not result in maximization of total profit.

media selection

31) The objective function of a diet problem is usually to ________ subject to nutritional requirements.

minimize costs

38) In a data envelopment analysis, it is customary to scale input process so that the total value of a unit's inputs equals ________.

one

27) Cranky Jerry's Furniture Factory makes tables and chairs. If he is interested in a profit maximizing level of production, he should probably follow the example for the ________ problem found in this chapter.

product mix

32) Investment problems maximize ________.

return on investments

30) The ________ for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign.

standard form

37) There are three plants scattered across the United States that manufacture Dull computers. These plants assemble products for customers throughout the United States, Canada, and Mexico. If Dull wishes to maximize profit by choosing the most economical pair of factory and customer for each order, they would be well-advised to follow the ________ model presented in this chapter.

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