AGEC 3413 test 3 (chapter 6 done and half of 7)

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107) Write the constraints for the 3 distribution centers.

x1A + x1B +x1c - 500y1 ≤ 0 x2A + x2B +x2c - 500y2 ≤ 0 x3A + x3B +x3c - 500y3 ≤ 0

84) If the optimal solution includes x11 = 100 and x22 = 200, determine the remaining shipments that will result in a minimum cost of $1700.

x31 = 150, x42 = 50

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region. (BETTER CHART IN DOCUMENT) Region DC A B C D 1 1 3 3 2 2 2 4 1 3 3 3 2 2 3 The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. 105) Define the decision variables for this situation.

y1 = 1 if DC1 is selected, 0 otherwise y2 = 1 if DC2 is selected, 0 otherwise y3 = 1 if DC3 is selected, 0 otherwise x1A = quantity shipped from DC 1 to Region A x1B = quantity shipped from DC 1 to Region B x1C = quantity shipped from DC 1 to Region C x1D = quantity shipped from DC 1 to Region D x2A = quantity shipped from DC 2 to Region A x2B = quantity shipped from DC 2 to Region B x2C = quantity shipped from DC 2 to Region C x2D = quantity shipped from DC 2 to Region D x3A = quantity shipped from DC 3 to Region A x3B = quantity shipped from DC 3 to Region B x3C = quantity shipped from DC 3 to Region C x3D = quantity shipped from DC 3 to Region D

116) What are the objective function terms that involve the demand locations?

$4DF + $4DG + $4DH + $10EF + $9EG + $8EH

118) Sketch the network for this problem and label all nodes and arrows with the appropriate information.

(picture you need to look at in the document)

88) Write the assignment problem matrix below as a network flow problem. Assume that the numbers in each cell represent the travel distance required between nodes. The dash indicates that there is not a route between nodes. (BETTER CHART IN DOCUMENT) A B C 1 4 6 - 2 - 2 1 3 3 5 9

(picture you need to look at in the document)

83) How many demand-side constraints are there? Write the demand-side constraints.

2 demand-side constraints x11 + x21 + x31 + x41 = 250 x12 + x22 + x32 + x42 = 250

Consider the following transportation problem: (BETTER CHART IN DOCUMENT) This one was a picture that didn't load 82) How many supply-side constraints are there? Write the supply-side constraints.

4 supply-side constraints x11 + x12 = 100 x21 + x22 = 200 x31 + x32 = 150 x41 + x42 = 50

37) In a balanced transportation model where supply equals demand: A) all constraints are equalities. B) none of the constraints are equalities. C) all constraints are inequalities. D) none of the constraints are inequalities.

47) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the: A) shortest route solution technique. B) minimal spanning tree solution method. C) maximal flow solution method. D) minimal flow solution method.

49) The first step in the shortest route solution method is to: A) select the node with the shortest direct route from the origin. B) determine all nodes directly connected to the permanent set nodes. C) arbitrarily select any path in the network from origin to destination. D) make sure that all nodes have joined the permanent set.

51) Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (node 1) to node 5? A) 13 B) 14 C) 15 D) 16

55) The first step of the minimal spanning tree solution method is to: A) select any starting node. B) select the node closest to the starting node to join the spanning tree. C) select the closest node not presently in the spanning tree. D) arbitrarily select any path in the network from origin to destination.

58) Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E. Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. What is the minimum number of paths (in tens of yards) that must be built to connect each facility? A) 54 B) 56 C) 60 D) 65

61) The horse walks from the Grass to the Pond and the llamas walk from the Fruit to the Shade. How much longer does the horse walk if each takes the shortest possible route? A) 60' B) 50' C) 40' D) 35'

66) Using the nodes of interest for the llamas, Fruit, Barn, Oak, Shade, Hay and Pond, what is the maximal flow from the Fruit to Hay? A) 11 B) 12 C) 13 D) 14

70) The constraint for Knoxville is: A) X14 + X24 + X34 - X43 - X45 - X46 - X47 = 0. B) X13 + X23 - X35 - X36 - X37 ≥ 0. C) X14 + X24 + X34 - X45 - X46 - X47 = 0. D) X14 + X24 + X34 + X43 + X45 + X46 + X47 ≥ 0.

72) The first step of the maximal flow solution method is to: A) arbitrarily select any path in the network from origin to destination. B) select the node with the shortest direct route from the origin. C) add the maximal flow along the path to the flow in the opposite direction at each node. D) select any starting node.

81) Which of these is the shortest route through the network? A) 1-3-6 B) 1-2-5-6 C) 1-4-5-6 D) 1-2-4-5-6

Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in figure below shows the possible routes and distances from the carpet plant in Valparaiso to the various warehouses or retail outlets. V = Valparaiso, P = Portage, G = Gary, Ha = Hammond, Hi = Highland, M = Merillville, L = Lansing 52) What is the distance for the shortest route from the carpet plant in Valparaiso to retail outlet in Lansing, Illinois. State the total completion time in minutes. A) 36 B) 37 C) 39 D) 41

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. 114) Write every constraint that involves Company A.

A's supply constraint is AD + AE = 200 D's balance constraint is AD + BD + CD - DF - DG - DH = 0 E's balance constraint is AE + BE + CE - EF - EG - EH = 0

117) How would the transshipment location constraints read if it was OK to store product there on a temporary basis?

AD + BD + CD - DF - DG - DH ≥ 0 AE + BE + CE - EF - EG - EH ≥ 0

41) In a network flow model, a directed branch: A) is a branch with a positive distance value. B) is a branch in which flow is possible in only one direction. C) is a branch on which the flow capacity is exhausted. D) is a branch in which flow is not possible in either direction.

43) A branch where flow is permissible in either direction is a(n): A) directed branch. B) undirected branch . C) labeled branch. D) unlabeled branch.

44) If we wanted to represent water resources as a network flow problem, which of the following would be represented as nodes? A) canals B) pumping stations C) rivers D) pipelines

48) In the linear programming formulation of the shortest route problem, the constraint for each node represents: A) capacity on each path. B) conservation of flow. C) capacity on each branch. D) minimum flow.

51) In a transportation problem, items are allocated from sources to destinations: A) at a maximum cost. B) at a minimum cost. C) at a minimum profit. D) at a minimum revenue.

53) Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso to retail outlet in Hammond. A) 26 B) 28 C) 30 D) 32

63) The llamas decide that a small system of trails would be perfect for connecting their points of interest, the Fruit, Barn, Hay, Shade, Pond and the Oak. What is the minimal total path length for this construction project? A) 275' B) 270' C) 265' D) 260'

69) Using all the nodes of interest for the entire menagerie, what is the maximal flow from Fruit to Hay? A) 16 B) 18 C) 20 D) 22

70) Using all the nodes of interest for the entire menagerie, what is the maximal flow from Grass to Pond? A) 20 B) 21 C) 22 D) 23

71) The objective of the maximal flow solution approach is to: A) maximize resource allocation. B) maximize the total amount of flow from an origin to a destination. C) determine the longest distance between an originating point and one or more destination points. D) determine the shortest distance between an originating point and one or more destination points.

72) What is the optimal solution to the Mantastic problem? A) $30,028 B) $30,820 C) $32,280 D) $32,820

73) The shortest route problem requires: A) each destination to be visited only once. B) finding the quickest route from the source to each node. C) that there be a branch from each destination to every other destination. D) that there be no two-way branches between nodes.

77) Which of these assignments is optimal? A) Dean 1 addresses Curriculum B) Dean 2 tackles Development C) Dean 3 solves Assessment D) Deans 2 and 3 both work on the Budget

79) Which of these is not an element of the objective function? A) 4DF B) 600D C) 9EG D) 3CE

80) What is the shortest route through the network in Figure 4. A) 16 B) 18 C) 20 D) 22

82) This network has been targeted for the innovative new "Elimination of Redundancy Elimination" program that offers a compromise between two competing factions. The plan is to remove paths one at a time until all of the nodes are interconnected without any loops in the network while minimizing the sum of all of the path lengths. Which of these paths is part of the new network? A) 3-6 B) 1-3 C) 1-2 D) 2-5

Comedy Pasture A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. 59) Llamas are pack animals and the owner occasionally has them tote supplies from the fruit trees down to the hay stand. What is the shortest route between the two? A) 150' B) 155' C) 160' D) 165'

40) Which term does not belong in an objective function for this scenario? A) 9WP B) 4XG C) 6XC D) 9ZG

42) In a network modeling problem, the linear programming decision variables are given by: A) source node. B) sink node. C) network branches. D) network nodes.

45) If we wanted to represent an office layout as a network flow problem, which of the following would be represented as a branch? A) offices B) waiting areas C) heating and ventilation systems D) computer rooms

46) If we wanted to represent an urban transportation system as a network flow problem, which of the following would be represented as nodes? A) streets B) railway lines C) street intersections D) pedestrian right of ways

48) David is qualified to teach Management Science, but has misplaced his slide rule and doesn't feel he can complete the necessary calculations if he is assigned to teach it next semester. Which of these constraints would ensure that he isn't the instructor? A) DI + DP + DQ + DC + DL ≥ 2 B) SM + GM + TM + DM ≤ 1 C) DM = 0 D) DI + DP + DQ + DC + DL + DM ≤ 3

56) The local Internet provider wants to develop a network that will connect its server at its satellite center in Valparaiso with the main city computer centers in Northwest Indiana to improve the Internet service and to minimize the amount of cable used to connect network nodes. If we represent this problem with a network: A) the cities are branches and cables are nodes. B) the cables are the branches and the cities are the nodes. C) the length of cables in miles are the branches, and the cities are the nodes. D) the cities are the branches and the length of cables in miles are the nodes.

57) Consider the network diagram given in Figure 2. Assume that the numbers on the branches indicate the length of cable (in miles) six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes? Figure 2 A) 16 miles B) 17 miles C) 18 miles D) 19 miles

60) Which of these routes for the horse is actually the shortest between the pair of nodes? A) Fruit - Hay = 160' B) Barn - Pond = 200' C) Grass - Pond = 190' D) Fruit - Shade = 165'

64) In the process of evaluating location alternatives, the transportation model method minimizes the: A) total demand. B) total supply. C) total shipping cost. D) number of destinations.

64) The llamas and horse spend most of their day wandering back and forth among their favorite spots in the yard, and have worn paths that are two feet wide among them. Amazingly, these paths correspond to a minimal spanning tree network! The property owner is fearful that the bare dirt paths will wash out during heavy rains, so he initiates a soil conservation project to lay sod over all of the bare dirt paths. How many square feet of sod must he purchase? A) 1080 B) 540 C) 680 D) 820

67) The difference between the assignment and the transportation problem is that: A) total supply must equal total demand in the assignment problem. B) the number of origins must equal the number of destinations in the transportation problem. C) each supply and demand value is 1 in the assignment problem. D) both A and B

68) Using the nodes of interest for the horse, Grass, Barn, Oak, Hay and Pond, what is the maximal flow from the Grass to Hay? A) 11 B) 12 C) 13 D) 14

76) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 4 to node 6 to node 8 to node 9. A) 2 B) 3 C) 4 D) 5

77) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 2 to node 7 to destination node 9. A) 3 B) 4 C) 5 D) 6

81) How many constraints are required to model this as a linear program? A) 8 B) 9 C) 10 D) 12

Comedy Pasture II A horse and two llamas are discussing the key areas of their domain on a lazy summer afternoon. The llamas favor the pond and shade and like to browse the fruit trees and oaks on the property, making their way to the barn only when their owner favors them with some oats. The horse prefers to graze the grass and hay for food and drink from the pond but will race up to the barn when the owner is handing out oats up there. Between the three of them, they have stepped off the distances between many of these key points several times and believe that they have developed an accurate map, shown below. This map shows the number of loads that can be hauled between all connected points on the property. As incredible as it may seem, neither the horse nor the llamas have had any training in management science, which is where you come in. 65) Using the nodes of interest for the llamas, Fruit, Barn, Oak, Shade, Hay and Pond, what is the maximal flow from the Barn to the Pond? A) 17 B) 18 C) 20 D) 23

Figure 4 78) Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches. A) 10 B) 12 C) 14 D) 16

41) What is the best overall fabulosity score that Mondo can hope for? A) 9 B) 25 C) 36 D) 45

46) Which constraint is appropriate for this scenario? A) DI + DP + DQ + DC + DL + DM = 2 B) SI + GI + TI + DI ≤ 6 C) SM + GM + TM + DM ≥ 1 D) SI + SP + SQ + SC + SL + SM ≤ 3

53) Which of the following assumptions is not an assumption of the transportation model? A) Shipping costs per unit are constant. B) There is one transportation route between each source and destination. C) There is one transportation mode between each source and destination. D) Actual total supply and actual total demand must be equal.

54) The minimal spanning tree problem determines the: A) minimum amount that should be transported along any one path. B) maximum amount that can be transported along any one path. C) shortest distance between a source node and a destination node. D) minimum total branch lengths connecting all nodes in the network.

62) The horse decides that a small system of trails would be perfect for connecting his points of interest, the Grass, Barn, Hay and Pond along with the Oak. What is the minimal total path length for this construction project? A) 295' B) 290' C) 280' D) 270'

67) Using the nodes of interest for the horse, Grass, Barn, Oak, Hay and Pond, what is the maximal flow from the Grass to Pond? A) 11 B) 12 C) 13 D) 14

71) The objective function is: A) MAX 4X13 + 25X14 + 22X23 + 3X24 - 3X34 - 3X43 - 20X35 - 30X36 - 40X37 - 6X45 - 15X46 - 20X47. B) MIN 4X13 + 25X14 + 22X23 + 3X24 - 3X34 - 3X43 - 20X35 - 30X36 - 40X37 - 6X45 - 15X46 - 20X47. C) MAX 4X13 + 25X14 + 22X23 + 3X24 + 3X34 + 3X43 + 20X35 + 30X36 + 40X37 + 6X45 + 15X46 + 20X47. D) MIN 4X13 + 25X14 + 22X23 + 3X24 + 3X34 + 3X43 + 20X35 + 30X36 + 40X37 + 6X45 + 15X46 + 20X47.

74) The maximal flow algorithm: A) does not require flow on every branch for the final solution. B) may end with capacity remaining at the source. C) may end with capacity at those nodes leading immediately to the destination. D) all of the above

76) Which of the following constraints represents the assignment for the curriculum task? A) X1C + X2C + X3C ≥ 1 B) X1C + X2C + X3C = 0 C) X1C + X2C + X3C = 1 D) X1C + X2C + X3C ≤ 1

79) Determine the minimum distance required to connect all nodes in Figure 4. A) 22 B) 24 C) 26 D) 30

Figure 2 50) Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (node 1) to node 4? A) 8 B) 9 C) 10 D) 11

Refer to the figure below to answer the following questions. Figure 3 75) Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9. A) 10 B) 11 C) 12 D) 13

10) In an unbalanced transportation problem, if demand exceeds supply, the optimal solution will be infeasible.

FALSE

11) The first step of the minimal spanning tree solution to compute the distance of any path through the network.

FALSE

13) In a minimal spanning tree, the source and destination nodes must be connected along a single path.

FALSE

14) The choice of the initial node in the minimal spanning tree technique must be the first node.

FALSE

15) The minimal spanning tree allows the visitation of each node without backtracking.

FALSE

16) The shortest route network problem could help identify the best plan for running cables for televisions throughout a building.

FALSE

18) Regardless of the number of nodes in a network, the minimal spanning tree cannot contain the two nodes with the greatest distance between them.

FALSE

20) The shortest route problem requires that there be a branch from each destination to every other destination.

FALSE

21) The maximal flow algorithm may end with capacity remaining at the source.

FALSE

5) Flows in a network can only be in one direction.

FALSE

7) In order to model a "prohibited route" in a transportation or transshipment problem, the route should be omitted from the linear program.

FALSE

8) A prohibited route in a transportation model should be assigned a value of zero.

FALSE

8) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the minimal spanning tree.

FALSE

86) If the optimal assignments include raking to Dolly, cooking to PJ, and mucking to Billy, what tasks are assigned to Jeffy and Thel?

Jeffy is assigned to the slaughter task and Thel receives the plucking task

115) What is the complete linear model for this scenario?

Min Z = $3AD + $3AE + $4BD + $3BE + $5CD + $3CE + $4DF + $4DG + $4DH + $10EF + $9EG + $8EH AD + AE = 200 BD + BE = 300 CD + CE = 500 DF + EF = 350 DG + EG = 450 EF + EH = 200 AD + BD + CD - DF - DG - DH = 0 AE + BE + CE - EF - EG - EH = 0 AD + BD + CD ≤ 600 AE + BE + CE ≤ 700

106) Write the objective function for this problem.

Min Z = 1x1A + 3x1B + 3x1C + 2x1D + 2x2A + 4x2B + 1x2C + 3x2D + 3x3A + 2x3B + 2x3C + 3x3D + 500y1 + 600y2 + 525y3

87) What are the linear programming constraints for mucking and Thel?

Mucking: XMB + XMD + XMJ + XMP+ XMT = 1 Thel: XRT + XCT + XMT + XPT+ XST = 1

1) A network is an arrangement of paths connected at various points through which items move.

TRUE

10) The minimal spanning tree problem is to connect all nodes in a network so that the total branch lengths are minimized.

TRUE

11) The transshipment model includes intermediate points between the sources and destinations.

TRUE

12) The last step of the minimal spanning tree solution method is to make sure all nodes have joined the spanning tree.

TRUE

14) In a transshipment problem, items may be transported from one transshipment point to another.

TRUE

15) In a transshipment problem, items may be transported from one destination to another.

TRUE

17) Regardless of the number of nodes in a network, the minimal spanning tree always contains the two nodes with the shortest distance between them.

TRUE

19) The goal of the maximal flow problem is to maximize the amount of flow of items from an origin to a destination.

TRUE

2) Nodes represent junction points connecting branches.

TRUE

22) The source node is the input node in a maximal flow problem.

TRUE

23) The maximal flow solution algorithm allows the user to choose a path through the network from the origin to the destination by any criteria.

TRUE

24) A traffic system could be represented as a network in order to determine bottlenecks using the maximal flow network algorithm.

TRUE

3) Branches connect nodes and show flow from one point to another.

TRUE

3) The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

TRUE

4) The values assigned to branches typically represent distance, time, or cost.

TRUE

6) For most real-world applications, an unbalanced transportation model is a more likely occurrence than a balanced transportation model.

TRUE

6) The shortest route problem is to find the shortest distance between an origin and various destination points.

TRUE

7) Once the shortest route to a particular node has been determined, that node becomes part of the permanent set.

TRUE

9) The shortest route network problem could help identify the best route for pizza delivery drivers from the pizza parlor to a specific customer.

TRUE

103) Mondo has never heard of linear programming and you don't have your laptop handy. Provide him with a "best case" total fabulosity number

The greatest possible value is 45, since there are 5 scores that will be chosen and the scores range from 1 to 9.

101) How many constraints does this model have? Provide a description in English for each one, without writing it mathematically.

The model has r + c or 10 constraints, not counting the nonnegativity constraint. The row constraints could be summarized as "Each model must wear one outfit," and the column constraints can be summarized as "Each outfit must be worn by a model." Individually, the constraints would be articulated as: Zoe must wear one outfit. Yvette must wear one outfit. Xena must wear one outfit. Whisper must wear one outfit. Vajay must wear one outfit. The gown must be worn. The sport outfit must be worn. The couture must be worn. The avant-garde must be worn. The prêt-à-porter outfit must be worn.

113) What special case of linear programming should be used to model this situation?

The scenario gives the appearance that it is an assignment model waiting to happen up until the point that six sections of Introduction to Operations are needed and the professors are responsible for two to three sections each. The easiest way to model this is by declaring it a transportation model with the six sections of Introduction to Operations as traveling to the same destination. However, if each of those six sections is a node unto itself, and if each professor is separated into three possible sources of teaching, then this would fit the assignment model. The problem with solving the scenario with an assignment model is that the number of decision variables increases from 24 to 132 and the constraints increase from 10 to 23.

102) Help Mondo make the best choice of outfit for each model using linear programming.

Using a Model-Outfit sequence for the decision variables yields the following: Max Fabulosity = 9ZG + 9ZS + 4ZC + 4ZA + 2ZP + 3YG + 8YS + 3YC + 8YA + 9YP + 4XG + 7XS + 3XC + 7XA + 8XP + 1WG + 6WS + 5WC + 6WA + 9WP + 4VG + 9VS + 9VC + 6VA + 7VP Subject to: ZG + ZS + ZC + ZA + ZP = 1 YG + YS + YC + YA + YP = 1 XG + XS + XC + XA + XP = 1 WG + WS + WC + WA + WP = 1 VG + VS + VC + VA + VP = 1 ZG + YG + XG + WG + VG = 1 ZS + YS + XS +WS +VS = 1 ZC + YC + XC + WC + VC = 1 ZA + YA + XA + WA + VA = 1 ZP + YP + XP + WP + VP = 1 ZG, ZS, ZC, ZA, ZP, YG, YS, YC, YA, YP, XG, XS, XC, XA, XP, WG, WS, WC, WA, WP, VG, VS, VC, VA, VP ≥ 0

111) The department chair is eager to motivate the senior faculty to consider retirement and wants to burden them as much as possible. What should the model look like that otherwise meets departmental objectives?

Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, Max Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM SI + SP + SQ + SC + SL + SM = 3 GI + GP + GQ + GC + GL + GM = 3 TI + TP + TQ + TC + TL + TM = 3 DI + DP + DQ + DC + DL + DM = 3 SI + GI + TI + DI ≥ 6 SP + GP + TP + DP = 1 SQ + GQ + TQ+ DQ = 1 SC + GC + TC + DC = 1 SL + GL + TL+ DL = 1 SM + GM + TM + DM = 1 The difference between this model and the benevolent chair model is that this is formulated to maximize prep time and assigns each professor a three-course load. The benevolent chair model minimizes prep time and allows for a two-course teaching load.

112) The department chair looks at past course evaluations and realizes that if she wants to attract students to the Operations and Supply Chain major, it would be best if Geoff were never assigned to teach that class. How can her standard model be modified to ensure that Geoff cannot scare away students from the major?

Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, these additions should be made to the base model. SI + TI + DI ≥ 6 GI = 0 The difference between this model and the base is that this assigns Geoff to no sections of Introduction to Operations, while maintaining he number of sections at six or greater among the other three faculty members. This model's objective is still to minimize the number of prep hours. As luck would have it, this model performs as well as the base model, which didn't have any sections of Intro assigned to Geoff.

110) Take note of the phrase in the scenario that reads "Naturally, every professor in the department had his own pet course..." Provide an example of a constraint that makes sure a professor gets to teach his favorite course.

Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops, we can ensure that Saba is assigned to Intro to Operations by entering the constraint: SI ≥ 2 along with the other constraints in the model. If Geoff likes Logistics, then GL = 1 would assign that professor the logistics class.

109) Write the model that is suitable for this scenario.

Using the scheme Professor:Subject for decision variables, e.g. SI is Saba teaches Intro to Ops: Min Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM SI + SP + SQ + SC + SL + SM ≤ 3 SI + SP + SQ + SC + SL + SM ≥ 2 GI + GP + GQ + GC + GL + GM ≤ 3 GI + GP + GQ + GC + GL + GM ≥ 2 TI + TP + TQ + TC + TL + TM ≤ 3 TI + TP + TQ + TC + TL + TM ≥ 2 DI + DP + DQ + DC + DL + DM ≤ 3 DI + DP + DQ + DC + DL + DM ≥ 2 SI + GI + TI + DI ≥ 6 SP + GP + TP + DP = 1 SQ + GQ + TQ+ DQ = 1 SC + GC + TC + DC = 1 SL + GL + TL+ DL = 1 SM + GM + TM + DM = 1

In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodes and between all intermediate nodes and all destinations for a given transshipment problem. In addition, assume that no travel is possible between source nodes, between intermediate nodes, and between destination nodes, and no direct travel from source nodes to destination nodes. Let the source nodes be labeled as 1, 2, 3, the intermediate nodes be labeled as 4 and 5, and the destination nodes be labeled as 6 and 7. 92) State the constraint for intermediate node 4.

X14 + X24 + X34 - X46 - X47 = 0

97) What is the constraint for El Paso for the Mantastic problem?

X37 + X47 = 610

104) You formulate this as an assignment model and review the Zoe section of the sensitivity analysis with Mondo. Provide him with an interpretation. (BETTER CHART IN DOCUMENT) Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease $J$13 Zoe Gown 1 0 9 1E+30 3 $K$13 Zoe Sport 0 0 9 3 2 $L$13 Zoe Leisure 0 -2 4 2 1E+30 $M$13 Zoe Cocktail 0 -5 4 5 1E+30 $N$13 Zoe Pret a Porter 0 -8 2 8 1E+30

Zoe is assigned to wear the gown and will add 9 points to the overall fabulosity score. Even if Zoe's rating in the gown was up to 3 points lower, she would still be assigned to wear the gown. The overall score would be lower, but this would still be her assignment. Normally, the reduced cost entries speak to the change in objective coefficients before the assignment changes. As the model was presented, the coefficient for Zoe in the Leisure outfit was 4, with a reduced cost of -2, so a change in excess of 4 to 4- -2 = 6 would cause the Leisure outfit assignment to be optimal. As this is a balanced model, we cannot make that statement.

26) In a network flow problem, ________ connect nodes and show flow from one point to another.

branches

27) In a network flow problem, the values assigned to ________ typically represent distance, time, or cost.

branches

33) The shortest route problem formulation requires a statement that mandates that what goes in to a node must equal what comes out of that node. This is referred to as ________.

conservation of flow

31) In a linear programming formulation of a transportation model, each of the possible combinations of supply and demand locations is a(n) ________.

decision variable

36) A one-way street in a downtown area should be modeled as a(n) ________ branch in a maximal flow model.

directed

37) In a typical network flow problem, the branches show flow from one node to the next. The nodes themselves are ________ points.

junction (connecting)

30) The goal of the ________ problem is to maximize the amount of flow of items from an origin to a destination.

maximal flow

31) A(n) ________ network model could be used to represent the capacity of a series of dams for flood control.

maximal flow

40) Determining where capacity needs to be added within a series of one-way roads within a park represents a(n) ________ model.

maximal flow

29) The ________ connects all nodes in a network so that the total branch lengths are minimized.

minimal spanning tree

35) Determining where to build roads at the least cost within a park that reaches every popular sight represents a(n) ________ network model.

minimal spanning tree

25) In a network flow problem, ________ represent junction points connecting branches.

nodes

36) In an assignment problem, all demand and supply values are equal to ________.

one

38) Once a decision maker has determined the shortest route to any node in the network, that node becomes a member of the ________.

permanent set

28) The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the ________ solution technique.

shortest route

34) A company plans to use an automatic guided vehicle for delivering mail to ten departments. The vehicle will begin from its docking area, visit each department, and return to the docking area. Cost is proportional to distance traveled. The type of network model that best represent this situation is ________.

shortest route

39) Determining where to build one way roads at the least cost within a park that takes visitors to every popular sight and returns them to the entrance represents a(n) ________ network model.

shortest route

32) A courier service located at the south edge of downtown dispatches three bicycle couriers with identical sets of architectural renderings that must go to three different downtown law offices as quickly as possible. This problem is a likely candidate for analysis using ________.

the shortest route solution/algorithm

22) In a(n) ________ problem, items are allocated from sources to destinations at a minimum cost.

transportation

26) The ________ model is an extension of the transportation model in which intermediate points are added between the sources and destinations.

transshipment

27) An example of a(n) ________ point is a distribution center or warehouse located between plants and stores.

transshipment

28) An appropriate choice of a model for analyzing the best shipping routes for a supply chain consisting of a manufacturer, warehouse, and retailer would be the ________ model.

transshipment

33) In most real-world cases, the supply capacity and demanded amounts result in a(n) ________ transportation model.

unbalanced

35) If the number of sources is greater than the number of destinations, then we have a(n) ________ assignment problem.

unbalanced

24) In an unbalanced transportation problem, if supply exceeds demand, the shadow price for at least one of the supply constraints will be equal to ________.

zero

Mantastic Devices designs and manufactures high-end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and Atlanta is 900 units. Demand at Memphis, New Orleans, and El Paso is 450, 500, and 610, respectively. The network representing the shipping routes is shown below. (picture you need to look at in the document) The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. (BETTER CHART IN DOCUMENT) Philadelphia Knoxville Memphis New Orleans El Paso Manhattan $4 $25 Atlanta $22 $3 Philadelphia $3 $20 $30 $40 Knoxville $3 $6 $15 $20 95) What is the objective function for the Mantastic problem? Use the notation Xij, where i and j correspond to the node numbers indicated in the diagram.

MIN 4X13 + 25X14 + 22X23 + 3X24 + 3X34 + 3X43 + 20X35 + 30X36 + 40X37 +

91) The committee would like to assign three reviewers to each applicant. A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign reviewers to Applicant B and Applicant C. (BETTER CHART IN DOCUMENT) Applicant Reviewer A B C 1 X 2 X 3 1 X 4 1 5 X 6 X 7 X 8 X 9 1 X

Multiple optimal solutions Applicant Reviewer A B C 1 0 0 1 2 0 1 0 3 1 0 0 4 1 0 0 5 0 1 0 6 0 0 1 7 0 0 1 8 0 1 0 9 1 0 0 Assigned 3 3 3 Applicant Reviewer A B C 1 1 0 0 2 0 1 0 3 1 0 0 4 0 0 1 5 0 1 0 6 1 0 0 7 0 0 1 8 0 1 0 9 0 0 1 Assigned 3 3 3

1) In a transportation problem, items are allocated from sources to destinations at a minimum cost.

TRUE

12) In a transshipment problem, items may be transported from sources through transshipment points on to destinations.

TRUE

13) In a transshipment problem, items may be transported from one source to another.

TRUE

16) In a transshipment problem, items may be transported directly from sources to destinations.

TRUE

17) In a transshipment problem, items may be transported from destination to destination and from source to source.

TRUE

18) An assignment problem is a special form of transportation problem where all supply and demand values equal 1.

TRUE

19) Assignment linear programs always result in integer solutions.

TRUE

4) In a balanced transportation model where supply equals demand, all constraints are equalities.

TRUE

9) A prohibited route in a transportation model should be assigned an arbitrarily high cost coefficient.

TRUE

99) What is the optimal solution for the Mantastic problem?

The lowest total cost is $30,820. X13 =710, X24 = 900, X34 = 710, X45 = 450, X46 = 550, X47 = 610

98) What is the total number of constraints for the Mantastic problem? How many decisions variables does it have?

There are seven constraints and twelve decision variables.

90) A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign two reviewers to Applicant B and 1 additional reviewer to Applicant C. (BETTER CHART IN DOCUMENT) Applicant Reviewer A B C 1 X 2 X 1 3 X 4 1 5 X 6 X 7 X 8 1 X 9 X Demand 2 2 2 Assigned 2

This is one possible solution. Another is to assign reviewer 9 to applicant C. Applicant Reviewer A B C 1 0 0 1 2 0 0 1 3 0 1 0 4 1 0 0 5 0 1 0 6 0 0 0 7 0 0 0 8 1 0 0 9 0 0 0 Demand 2 2 2 Assigned 2 2 2

The patriarch of the least funny comic strip in the history of the world must assign loathsome tasks to his children and spouse. Time estimates, based on historical performance, are provided in the table. (BETTER CHART IN DOCUMENT) Rake Cook Muck Pluck Slaughter Billy 12 10 10 16 13 Dolly 9 10 14 13 10 Jeffy 17 14 12 18 12 PJ 15 7 11 11 18 Thel 13 18 22 11 27 85) Using the data in the table: a) How many supply-side constraints are needed? b) How many demand-side constraints are needed? c) How many decision variables are involved in this assignment method?

a) 5, b) 5, c) 25

39) What is an appropriate constraint for this scenario? A) ZG + YG + XG + WG + VG ≤ 1 B) ZG + YG + XG + WG + VG = 1 C) 9ZG + 3YG + 4XG + 1WG + 4VG ≥ 1 D) 9ZG + 3YG + 4XG + 1WG + 4VG = 1

42) Mondo ran the problem in Excel and has copied a portion of the sensitivity report below. (look at document for better chart) Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase AllowableDecrease $J$13 Zoe Gown 1 0 9 1E+30 3 $K$13 Zoe Sport 0 0 9 3 2 $L$13 Zoe Leisure 0 -2 4 2 1E+30 $M$13 Zoe Cocktail 0 -5 4 5 1E+30 $N$13 Zoe Pret a Porter 0 -8 2 8 1E+30 What is a reasonable conclusion that can be drawn from this section of the report? A) Zoe will contribute 9 points to the overall fabulosity score of the model. B) It doesn't matter whether Zoe wears the sport outfit or the gown. C) The sport outfit has a range of 5 in fabulosity. D) Wearing the cocktail dress would lower the overall fabulosity score by 5 points.

47) Which constraint ensures that Introduction to Operations is offered according to the scenario? A) SI + GI + TI + DI ≥ 6 B) SI + GI + TI + DI ≤ 6 C) SI + SP + SQ + SC + SL + SM ≤ 6 D) SI + SP + SQ + SC + SL + SM ≥ 6

57) Which of the following are assumptions or requirements of the transportation problem? A) There must be multiple sources. B) Goods are the same, regardless of source. C) There must be multiple destinations. D) There must be multiple routes between each source and each destination.

63) In an assignment problem all supply and demand values equal are: A) 0. B) 1. C) 2. D) greater than 1.

65) The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means: A) agent 3 can be assigned to 2 tasks. B) agent 3 can be assigned to no more than 2 tasks. C) a mixture of agents 1, 2, 3 and 4 will be assigned to tasks. D) agents 1, 2, 3, and 4 can be assigned up to 2 tasks.

66) In an assignment problem: A) one agent can do parts of several tasks. B) one task can be done by only one agent. C) each agent is assigned to its own best task. D) several agents can do parts of one task.

69) The constraint for the quantity shipped from Atlanta is: A) X23 + X 24 = 1000. B) X23 + X 24 ≤ 1000. C) X23 + X 24 ≥ 1000. D) X13 + X 14 - X34 = 1000.

73) Which of these changes in the original formulation of the Mantastic problem will result in no transfer of product from Philadelphia to Knoxville? A) increasing the cost to ship product from Philadelphia to Knoxville to $14 per unit. B) lowering the cost to ship product from Philadelphia to New Orleans to $12 per unit. C) increasing the cost to ship product from Philadelphia to Knoxville to $16 per unit. D) lowering the cost to ship product from Philadelphia to either New Orleans or Memphis to $12 per unit.

29) A form of the transportation problem in which all supply and demand values equal 1 is the ________ problem.

assignment

30) A plant has four jobs to be assigned to four machines, and each machine has different manufacturing times for each product. The production manager wants to determine the optimal assignments of four jobs to four machines to minimize total manufacturing time. This problem can be most efficiently solved using the ________ model.

assignment

60) In a transshipment problem, items may be transported: A) from destination to destination. B) from one transshipment point to another. C) directly from sources to destinations. D) all of the above

62) Which constraint represents the quantity shipped to retail outlet 6? A) X23 + X36 = 450 B) X23 + X36 + X26 = 450 C) X36 + X26 ≤ 450 D) X36 + X26 = 450 E) 3X36 + 5X26 = 450

80) How many decision variables are in this problem? A) 8 B) 9 C) 10 D) 12

56) The assignment problem constraint x41 + x42 + x43 + x44 ≤ 3 means: A) agent 3 can be assigned to 4 tasks. B) agent 4 can be assigned to 3 tasks. C) a mixture of agents 1, 2, 3 and 4 will be assigned to tasks 1, 2 or 3. D) There is no feasible solution.

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. 78) Which of these constraints allows for some inventory to be held at one of the crossdock facilities? A) AD + BD + CD - DF - DG - DH ≥ 0 B) AD + BD + CD - DF - DG - DH = 600 C) AD + BD + CD = DF - DG - DH = 600 D) AD + BD + CD + DF + DG + DH = 600

Mondo's Runway Show Mondo Guerra is matching his models with his latest collection for Fashion Week. He has five models, ranging from 5'10" to 5'10.5" and size 0 to size 1. His five latest designs run the gamut from prêt-à-porter to an evening gown and he'd like to make sure each outfit looks as good as possible by having it worn on the runway by the right model. After an anxious month of sewing, he has each model try on each outfit and he assigns a fabulosity score to each combination as indicated in the table. (look at document for better chart) Gown Sport Couture Avant Garde Prêt-à-Porter Zoe 9 9 4 4 2 Yvette 3 8 3 8 9 Xena 4 7 3 7 8 Whisper 1 6 5 6 9 Vajay 4 9 9 6 7 38) What is an appropriate constraint for this scenario? A) ZG + ZS + ZC + ZA + ZP = 1 B) ZG + ZS + ZC + ZA + ZP ≤ 1 C) 9ZG + 9ZS + 4ZC + 4ZA + 2 ZP ≥ 1 D) 9ZG + 9ZS + 4ZC + 4ZA + 2 ZP = 1

43) Mondo ran the problem in Excel but used "≤ 1" constraints everywhere instead of "= 1" constraints. The objective function is formulated correctly and the general structure of the constraints is also correct, except for the inequality. What is a reasonable conclusion that can be drawn from this formulation of the model? A) None of the outfits will be worn. B) There would be no difference in the model results from one with = constraints. C) A model may be assigned two different outfits. D) An outfit may be assigned to two different models.

49) Copied below is a portion of the answer report that shows the constraints related to the faculty assignment. Which of these statements is best according to the answer report? (look at document for better chart) Cell Name Cell Value Formula Status Slack $S$15 Saba_assigned 3 $S$15<=$Q$15 Binding 0 $S$15 Saba_assigned 3 $S$15>=$T$15 Not Binding 1 $S$16 Geoff_assigned 3 $S$16<=$Q$16 Binding 0 $S$16 Geoff_assigned 3 $S$16>=$T$16 Not Binding 1 $S$17 Tim_assigned 2 $S$17<=$Q$17 Not Binding 1 $S$17 Tim_assigned 2 $S$17>=$T$17 Binding 0 $S$18 David_assigned 3 $S$18<=$Q$18 Binding 0 A) Geoff is assigned to teach Introduction to Operations. B) Tim is assigned to teach two courses. C) David is assigned to teach Management Science. D) Saba is assigned to teach two courses.

Mantastic Devices designs and manufactures high-end support garments for men. The facilities in Manhattan and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Memphis, New Orleans, or El Paso. Manufacturing capacity in Manhattan and Atlanta is 900 units. Demand at Memphis, New Orleans, and El Paso is 450, 500, and 610, respectively. The network representing the shipping routes is shown below. (picture you need to look at in the document) The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. (BETTER CHART IN DOCUMENT) Philadelphia Knoxville Memphis New Orleans El Paso Manhattan $4 $25 Atlanta $22 $3 Philadelphia $3 $20 $30 $40 Knoxville $3 $6 $15 $20 68) The transshipment locations are: A) Manhattan and Atlanta. B) Philadelphia and Knoxville. C) Manhattan, Atlanta, Philadelphia and Knoxville. D) Memphis, New Orleans, and El Paso.

Semester Prep The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below. (look at document for better chart) Intro to Ops Project Mgt Quality Mgt Control Logistics Mgt Science Saba 3 10 12 16 12 7 Geoff 4 19 2 10 8 18 Tim 5 11 4 14 14 3 David 4 11 4 15 17 15 45) What is an appropriate objective function for this scenario? A) Max Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM B) Min Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM + 5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM C) Min Z = SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM + TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM D) Max Z = SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM + TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM

44) Mondo ran the problem in Excel but wondered what would happen if he allowed his favorite model Xena to wear two outfits. She would be the first to walk the runway, then would change and also be the last model in the show. The sensitivity analysis for the original problem scenario is shown below. (look at document for better chart) Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease $J$20 Gown 1 8 1 0 1 $K$20 Sport 1 8 1 0 1 $L$20 Leisure 1 5 1 0 0 $M$20 Cocktail 1 8 1 0 1 $N$20 Pret_a_Porter 1 9 1 0 1 $P$13 Zoe_wears 1 1 1 1 0 $P$14 Yvette_wears 1 0 1 1 0 $P$15 Xena_wears 1 -1 1 1 0 $P$16 Whisper_wears 1 0 1 0 1E+30 $P$17 Vajay_wears 1 4 1 0 0 What would happen if Mondo ran the model again, but this time changed the existing constraints to ≤ constraints and included a constraint that required Xena to model two separate looks? A) Xena would wear the pret-a-porter and the gown. B) Xena would wear the pret-a-porter and the cocktail. C) The overall fabulosity score would drop by 1. D) Xena would keep the same outfit.

50) Copied below is a portion of the answer report that shows the status of the variable cells related to the faculty assignment. Which of these statements is consistent with the answer report? (look at document for better chart) Cell Name Original Value Final Value Integer $J$15 Saba Intro 1 2 Contin $K$15 Saba Project Mgt 1 0 Contin $L$15 Saba Quality Control 1 0 Contin $M$15 Saba Planning/Control 1 0 Contin $N$15 Saba Logistics 1 0 Contin $O$15 Saba Mgt Science 1 1 Contin $J$16 Geoff Intro 1 0 Contin A) Geoff is assigned to teach Introduction to Operations. B) Tim is assigned to teach two courses. C) David is assigned to teach Introduction to Operations D) Saba is assigned to teach two courses.

54) The problem that deals with the distribution of goods from several sources to several destinations is the: A) network problem. B) assignment problem. C) transportation problem. D) transshipment problem.

75) Which of the following constraints represents the assignment for assistant dean 2? A) X2A + X2B + X2C + X2D ≤ 1 B) X2A + X2B + X2C + X2D = 0 C) X2A + X2B + X2C + X2D = 1 D) X2A + X2B + X2C + X2D ≥ 0

An interim dean needs help from three assistant deans after the dean and associate dean were transferred back to full-time faculty. The estimated time for each assistant dean to do each task is given in the matrix below. (BETTER CHART IN DOCUMENT) Assessment Budget Curriculum Development Assistant 1 44 54 42 45 Assistant 2 48 50 64 47 Assistant 3 46 56 64 72 74) How many tasks will be assigned to the assistant deans? A) 1 task B) 2 tasks C) 3 tasks D) 4 tasks

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2. (picture you need to look at in the document) Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. 61) Which constraint represents transshipment through the distribution center? A) 2X13 + 3X23 = 900 B) 2X13 + 3X23 + 5X34 + 4X35 + 3X36 = 0 C) X13 + X23 - X34 - X35 - X36 = 0 D) X13 + X23 - X34 - X35 - X36 ≥ 0

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C. 58) The constraint that represents the quantity supplied by DC 1 is: A) 4X1A + 6X1B + 8X1C ≤ 500. B) 4X1A + 6X1B + 8X1C = 500. C) X1A + X1B + X1C ≤ 500. D) X1A + X1B + X1C = 500.

59) The constraint that represents the quantity demanded by Customer B is: A) 6X1B + 2X2B + 8X3B ≤ 350. B) 6X1B + 2X2B + 8X3B = 350. C) X1B + X2B + X3B ≤ 350. D) X1B + X2B + X3B = 350.

52) The linear programming model for a transportation problem has constraints for supply at each ________ and ________ at each destination. A) destination, source B) source, destination C) demand, source D) source, demand

55) In the linear programming formulation of a transportation network: A) there is one variable for each arc. B) there is one constraint for each node. C) the sum of variables corresponding to arcs out of a source node is constrained by the supply at that node. D) All of these statements are correct for the linear programming formulation.

2) In a transportation problem, items are allocated from sources to destinations at a maximum value.

FALSE

21) In a transshipment model, the supply at each source and demand at each destination are limited to one unit.

FALSE

5) In an unbalanced transportation model, all constraints are equalities.

FALSE

Mondo's Runway Show Mondo Guerra is matching his models with his latest collection for Fashion Week. He has five models, ranging from 5'10" to 5'10.5" and size 0 to size 1. His five latest designs run the gamut from prêt-à-porter to an evening gown and he'd like to make sure each outfit looks as good as possible by having it worn on the runway by the right model. After an anxious month of sewing, he has each model try on each outfit and he assigns a fabulosity score to each combination as indicated in the table. (BETTER CHART IN DOCUMENT) Gown Sport Couture Avant Garde Prêt-à-Porter Zoe 9 9 4 4 2 Yvette 3 8 3 8 9 Xena 4 7 3 7 8 Whisper 1 6 5 6 9 Vajay 4 9 9 6 7 100) What is an appropriate objective function for this scenario?

Using a Model-Outfit sequence for the decision variables yields the following: Max Fabulosity = 9ZG + 9ZS + 4ZC + 4ZZA + 2ZP + 3YG + 8YS + 3YC + 8YA + 9YP + 4XG + 7XS + 3XC + 7XA + 8XP + 1WG + 6WS + 5WC + 6WA + 9WP + 4VG + 9VS + 9VC + 6VA + 7VP

96) What is the constraint for the transshipment node in Philadelphia for the Mantastic problem?

X13 + X23 + X43 — X34 - X35 - X36 - X37 = 0

89) Awards committees need to be formed to review potential award recipients. In the past, three people have been assigned to review each applicant. The only stipulation is that a reviewer cannot be assigned to an applicant if the applicant is a co-worker. The matrix below shows 9 reviewers, 3 candidates, and a matrix. If an entry in the matrix contains an "X," then that specific reviewer is ineligible to review an applicant's material. For example, reviewer 1 cannot review materials submitted by candidate B. It is possible that some reviewers may not receive an assignment. (BETTER CHART IN DOCUMENT) Applicant Reviewer A B C 1 X 2 X 3 X 4 5 X 6 X 7 X 8 X 9 X Formulate this as an assignment problem in which two reviewers are assigned to review each applicant's material.

X1A + X1B + X1C ≤ 1 X2A + X2B + X2C ≤ 1 X3A + X3B + X3C ≤ 1 X4A + X4B + X4C ≤ 1 X5A + X5B + X5C ≤ 1 X6A + X6B + X6C ≤ 1 X7A + X7B + X7C ≤ 1 X8A + X8B + X8C ≤ 1 X9A + X9B + X9C ≤ 1 X1A + X3A + X4A + X6A + X7A + X8A + X9A = 2 X2B + X3B + X4B + X5B + X8B = 2 X1C + X2C + X4C + X5C + X6C + X7C + X9C = 2

93) If there are 300 units available at source 2, state the constraint for source node 2.

X24 + X25 = 300

94) If there are 175 units demanded at destination 6, state the constraint for destination 6.

X46 + X56 = 175

23) In a(n) ________ transportation model where supply equals demand, all constraints are equalities.

balanced

34) In order to prevent the accumulation of inventory at transshipment points, they should be modeled as being ________ nodes.

balanced

25) In order to model a "prohibited route" in a transportation or transshipment problem, the cost assigned to the route should be ________.

high

32) The cost to send a unit of product from supply source A to demand location B would be represented in the ________ of the linear programming statements.

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