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operations research an introduction

Questions and Answers of Operations Research An Introduction

36 Explain how your formulation in Problem 35 changes if both of the following conditions are added:a The number of Type 1 layouts cannot exceed the number of Type 2 layouts.b There must be at least
37 Graphically solve the following LP problem: min z = 6x1 + 2x2 s.t. 3x + 2x2 12 2x + 4x2 12 10
38 We produce two products: product 1 and product 2 on two machines (machine 1 and machine 2). The number of hours of machine time and labor depends on the machine and the product as shown in Table
39 Carrotco manufactures two products: 1 and 2. Each unit of each product must be processed on machine 1 and machine 2 and uses raw material 1 and raw material 2. The resource usage is as in Table
40 A company assembles two products: A and B. Product A sells for $11 per unit, and product B sells for $23 per unit.A unit of product A requires 2 hours on assembly line 1 and 1 unit of raw
41 Ann and Ben are getting divorced and want to determine how to divide their joint property: retirement account, home, summer cottage, investments, and miscellaneous assets. To begin, Ann and Ben
42 Eli Daisy manufactures two drugs in Los Angeles and Indianapolis. The cost of manufacturing a pound of each drug is shown in Table 70.The machine time (in hours) required to produce a pound of
43 Daisy also produces Wozac in New York and Chicago.Each month, it can produce up to 30 units in New York and up to 35 units in Chicago. The cost of producing a unit each month at each location is
44 You have been put in charge of the Dawson Creek oil refinery. The refinery produces gas and heating oil from crude oil. Gas sells for $11 per barrel and must have an average grade level of at
45 Currently we own 100 shares each of stocks 1 through 10. The original price we paid for these stocks, today’s price, and the expected price in one year for each stock is shown in Table 76.We
46 Gotham City National Bank is open Monday–Friday from 9 A.M. to 5 P.M. From past experience, the bank knows that it needs the number of tellers shown in Table 77. The bank hires two types of
47 The Gotham City Police Department employs 30 police officers. Each officer works 5 days per week. The crime rate fluctuates with the day of the week, so the number of police officers required each
48 Alexis Cornby makes her living buying and selling corn.On January 1, she has 50 tons of corn and $1,000. On the first day of each month Alexis can buy corn at the following prices per ton:
49 At the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 78). Any money left over may
50 City 1 produces 500 tons of waste per day, and city 2 produces 400 tons of waste per day. Waste must be incinerated at incinerator 1 or 2, and each incinerator can process up to 500 tons of waste
51 Silicon Valley Corporation (Silvco) manufactures transistors. An important aspect of the manufacture of transistors is the melting of the element germanium (a major component of a transistor) in a
52 A paper-recycling plant processes box board, tissue paper, newsprint, and book paper into pulp that can be used to produce three grades of recycled paper (grades 1, 2, and 3). The prices per ton
53 Turkeyco produces two types of turkey cutlets for sale to fast-food restaurants. Each type of cutlet consists of white meat and dark meat. Cutlet 1 sells for $4/lb and must consist of at least 70%
54 Priceler manufactures sedans and wagons. The number of vehicles that can be sold each of the next three monthsare listed in Table 83. Each sedan sells for $8,000, and each wagon sells for $9,000.
55 The production-line employees at Grummins Engine work four days a week, 10 hours a day. Each day of the week, (at least) the following numbers of line employees are needed: Monday–Friday, 7
56 Bank 24 is open 24 hours per day. Tellers work two consecutive 6-hour shifts and are paid $10 per hour. The possible shifts are as follows: midnight–6 A.M., 6 A.M.–noon, noon–6 P.M., 6
57 Transeast Airlines flies planes on the following route:L.A.–Houston–N.Y.–Miami–L.A. The length (in miles) of each segment of this trip is as follows: L.A.–Houston, 1,500 miles;
58 To process income tax forms, the IRS first sends each form through the data preparation (DP) department, where information is coded for computer entry. Then the form is sent to data entry (DE),
59 In the electrical circuit of Figure 11, It = current (in amperes) flowing through resistor t, Vt = voltage drop (in volts) across resistor t, and Rt = resistance (in ohms) of resistor t.
60 The mayor of Llanview is trying to determine the number of judges needed to handle the judicial caseload.During each month of the year it is estimated that the number of judicial hours needed is
61 E.J. Korvair Department Store has $1,000 in available cash. At the beginning of each of the next six months, E.J.will receive revenues and pay bills as shown in Table 85. It is clear that E.J.
62 Olé Oil produces three products: heating oil, gasoline, and jet fuel. The average octane levels must be at least 4.5 for heating oil, 8.5 for gas, and 7.0 for jet fuel. To produce these products
63 Donald Rump is the international funds manager for Countribank. Each day Donald’s job is to determine how the bank’s current holdings of dollars, pounds, marks, and yen should be adjusted to
Consider the following graph.Numbers on arcs and edges represent lengths.(a) Identify the nodes, arcs, and edges of the graph.(b) Determine whether each of the following sequences is a path of the
Do Exercise 9-1 for the graphand sequences 3–2–4–5, 3–2–1–4, 1–3–5–2–4, 1–3–2–5. 1 8 00 2 15 4 3. 10 1 3 8 00 5
Consider the following graph.(a) Find (by inspection) shortest paths from all nodes to all other nodes.(b) Verify that every subpath of the optimal 1 to 4 path in part (a) is itself optimal.(c)
Do Exercise 9-5 for the following graph, verifying the optimal 4 to 2 path in part (b). 8 2 6 5 3
Consider the following digraph:Numbers on arcs represent costs.(a) Find (by inspection) shortest paths from node 1 to all other nodes.(b) Enumerate the dicycles of the graph.(c) Determine whether
Do Exercise 9-7 for the digraph 1 -20 11 2 3 10 2
For each of the following digraphs, determine which of Bellman–Ford Algorithms 9A, Floyd–Warshall Algorithm 9B, and Dijkstra Algorithm 9C could be applied to compute shortest paths from node 1 to
Demonstrate whether each of the following digraphs is acyclic by exhibiting a dicycle or numbering nodes so that every arc 1i, j2 has i 6 j. (a) d (b) b (c)
Consider the following digraph:Suppose that labels on arcs are cost and that we seek a minimum total cost path from node 1 to all other nodes.(a) Demonstrate that acyclic shortest path Algorithm 9D
Do Exercise 9-19 for the digraph 4 -10 2 -2 -5 6 11 2 -16 3 5
The digraph below shows an instance of the shortest path problem. Numbers on the arcs are lengths. We wish to compute a shortest path from the indicated node s to the indicated node t.(a) Which of
The table that follows lists the tasks that must be performed in preparing a simple breakfast.The table also shows the number of minutes each requires and the tasks that must be completed before each
The table that follows lists the activities that must be performed in organizing a soccer tournament.The table also shows the estimated number of days that each will require and the activities that
Officers of Industrial Engineering student organizations are planning the annual awards banquet. The following table shows the major activities of the project, along with their durations(in days) and
Construction of a small two-story house involves the tasks listed in the following table.The table also shows the estimated duration of each task in days and the tasks that must completed before it
The figure that follows shows a partially complete layout for a circuit board of a large computer peripheral. Lines show channels along which circuits can be placed, together with the lengths of the
The figure that follows shows the links of a proposed campus computer network. Each node is a computer, and links are fiber-optic cable.Designers now want to decide how E-mail, which will be broken
The machine shop depicted in the figure that follows has a heat treatment workstation at point 1, forges at points 2 and 3, machining centers at points 4, 5, and 6, and a grinding machine at 7.Each
The figure that follows shows the trails of Littleville’s Memorial Park.Whenever there is a major event there, heavy hot dog and soft-drink carts are stored in the shed and rolled out along the
Two promising drugs—X14Alpha and X14Beta—are ready for testing to combat rare, but dangerous virus X14. If one of the drugs proves to have high effectiveness, 500 lives could be saved in the
Saw King (SK) is the region’s leading seller of the highest rated model of chain saws. Their challenge is that their present store site has space for only an inventory of 18 of the very large saws.
Each of the following depicts a minimum cost network flow problem, with labels on nodes indicating net demand and those on arcs showing unit cost and capacity. Determine for each (without solving)
Consider the following digraph.(a) Exhibit the Node–Arc Incidence Matrix (NAIM) of this digraph.(b) Select a column submatrix of your NAIM with the maximum possible number of linearly independent
The Quick Chip gravel company has received a contract to supply two new construction projects in the towns of Brock and Wurst. A total of 60 truckloads are needed at Brock in the next month and 90 at
The table below shows the results of triaging 7 persons injured in a recent terrorist attack.Each patient has been scored (1 = lowest to 5 = highest) according the compatibility of his/her needs vs.
Senior design students are negotiating which of the four members of the team will take primary reponsibility for each of the four project tasks the team must complete. The following table shows the
Consider the following digraph.(a) Starting from an all zero flow, apply Bellman Ford Algorithm 10E to compute a max flow from node s to node t. Show the residual digraph at each iteration, and
Consider the following undirected graph, taking numbers on edges as costs/weights.(a) Apply standard Greedy Algorithm 10F to compute a maximum spanning tree of the graph.(b) Sketch a tree like Figure
The following graph shows an instance of the Maximum Spanning Tree Problem.Do (a)–(f) of Exercise 10-50. 11 1 3 13 17. 2 4 15 19
The Metropolis Regional Authority (MRA)is planning the construction of a light rail network connecting the major activity centers of the region.The figure below shows the 9 centers involved along
The figure that follows shows a part of a distribution network like those used by Shell Oil Company16 to supply the midwest with its three main classes of product: gasoline, kerosene/jet fuel, and
A fertilizer plant can make a product by any of 3 processes. Using decision variables xj !number of units produced by process j, the following linear program computes a minimum cost way to produce
A computer distributor can purchase workstations from any of 3 suppliers. Using decision variables xj!number of units purchased from supplier j, the following linear program computes a minimum cost
A retired executive has up to $8 million that he wishes to invest in apartment buildings. The following table shows the purchase price and the expected 10-year return (in millions of dollars) of the
The River City redevelopment authority wants to add a minimum of one thousand new parking spaces in the downtown area. The following table shows the estimated cost (in millions of dollars) of the 4
Silo State’s School of Engineering is preparing a 5-year plan for building construction and expansion to accommodate new offices, laboratories, and classrooms. The Electrical Engineering faculty
A small pharmaceutical research laboratory must decide which product research activities to undertake with its $25 million available in each of the next two 5-year periods. The products optamine and
The map that follows shows the locations of 8 applicants for low-power radio station licences and the approximate range of their signals.Regulators have scored the quality of applications on a scale
Time Sink Incorporated is about to begin selling its computer game software to college students in the midwest. The following table shows the states that could be covered by salespersons based at 4
The following map shows the 8 intersections at which automatic traffic monitoring devices might be installed. A station at any particular node can monitor all the road links meeting that
Top Tool Company wishes to hire parttime models to pass out literature about its machine tools at an upcoming trade show. Each of the 6 available models can work 2 of the 5 show days:
Air Anton is a small commuter airline running 6 flights per day from New York City to surrounding resort areas. Flight crews are all based in New York, staffing flights to various locations and then
A special court commission appointed to resolve a bitter fight over legislative redistricting has proposed 6 combinations of the 5 disputed counties that could form new districts. The following table
Mogul Motors is planning a major overhaul of its automobile assembly plants as it introduces 4 new models. Exactly one exisiting plant must be converted to assemble each model. The following table
The sister communities program pairs cities in Russia with cities in the United States that have a similar size and economic base. Visits are then exchanged between the sister communities to improve
The following table shows the unit price and the minimum quantity at which suppliers j = 1c, 5 have to bid to supply State University(SU) with office desk chairs. SU wishes to find the lowest total
Channel 999 TV has staff to provide onscene coverage of up to 4 high school football games this Friday. The following table shows 3 possibilities are in the town where Channel 999 is located. At
Erika Entrepreneur assembles laptop computer systems in her home to finance her graduate education. She makes and sells two types of units, both using the same frame. The deluxe model has 1024
Sandbox State University is rearranging the locations of 3 equal-sized academic departments to provide for better faculty communication.The following tables show the estimated number of
The River City Operations Research society is planning a meeting that will have 2 morning and 2 afternoon sessions running at the same time. The 4 sessions will be on LP, NLP, ILP, and INLP,
A warehouse facility has packing stations at both its front and back entrances. The following table shows the number of ton-feet (in thousands) of materials handling that would be required to move
Three professional baseball teams are trying to find places for 6 available players within their remaining salary limits of $35 million, $20 million, and $26 million, respectively. The following
Small business Cool Room Furniture(CRF) sells whole-room packages of furniture in the region around its single store and warehouse.Each day it must decide how to assign needed deliveries i = 1,c, m
Military commanders are planning the command structure for 6 new radar stations.Three commanders will each be in charge of two of the stations. The following table shows the projected cost (in
Awesome Advertising manages the television promotion of a variety of products. In the next few months they are planning to crossadvertise six of their items by running interlocking television ads
Engineers are designing a fixed route to be followed by automatic guided vehicles in a large manufacturing plant. The following table shows the east–west and north–south coordinates of the 6
An oil company currently has 5 platforms drilling off the Gulf coast of the United States.The following table shows the east–west and north–south coordinates of their shore base at point 0 and
Every week Mighty Mo Manufacturing makes one production run of each of its 4 different kinds of metal cookware. Setup times to make any particular product vary depending on what was produced most
Every weekday afternoon, at the height of the rush hour, a bank messenger drives from the a bank’s central office to its 3 branches and returns with noncash records of the day’s activity.The
Gotit Grocery Company is considering 3 locations for new distribution centers to serve it customers in 4 nearby cities. The following table shows the fixed cost (in millions of dollars) of opening
Basic Box Company is considering 5 new box designs of different sizes to package 4 upcoming lines of computer monitors. The following table shows the wasted space that each box would have if used to
The figure that follows shows 5 pipelines under consideration by a natural gas company to move gas from its 2 fields to its 2 storage areas.The numbers on the arcs show the number of miles of line
Dandy Diesel manufacturing company assembles diesel engines for heavy construction equipment. Over the next 4 quarters the company expects to ship 40, 20, 60, and 15 units, respectively, but no more
Top-T shirt company imprints T-shirts with cartoons and celebrity photographs. For each of their 4 pending contracts, the following table shows the number of days of production required, the earliest
Sarah is a graduate student who must make 4 large experimental runs on her personal computer as part of her thesis research. The jobs require virtually all the computer’s resources, so only one can
Three new jobs have just arrived at Fancy Finishing’s main furniture restoration shop. The following table shows the sequence that each must follow through the company’s 3 finish removal
A team of auditors has divided itself into 3 groups, each to examine one category of records.Each group will review their speciality area for all 3 subsidiaries of the client being audited, but the
With the addition of a new plant, Monsanto9 now has more capacity than it needs to manufacture its main chemical product. Numerous reactors i = 1,c, m can be operated at a variety j = 1,c, n of
W.R. Grace10 strip mines phosphates in strata numbered from i = 1 at the top to i = n at the deepest level. Each stratum must be removed before the next can be mined, but only some of the layers
Ault Food Limited11 is planning the production and distribution system for its new line of food products. Plants may be opened at any of sites i = 1,c, 7, and warehouses at locations j = 1,c, 13, to
Space structures12 designed for zero gravity have no structural weight to support and nothing to which a foundation can be attached.The structure needs only to withstand vibrations in space. This is
The National Cancer Institute13 has received proposals from 22 states to participate in its newest smoking intervention study. The first j = 1,c, 5 are from the Northeast region, the next j = 6,c, 11

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