Question: A company manufactures three products: A, B,

> Caro-Life is a financial services firm that specializes in selling life, auto, and home insurance to residential consumers in the state of North Carolina. The company is planning to expand and offer its services in South Carolina as well. The company wan

> The Molokai Nut Company (MNC) makes four different products from macadamia nuts grown in the Hawaiian Islands: chocolate-coated whole nuts (Whole), chocolate-coated nut clusters (Cluster), chocolate-coated nut crunch bars (Crunch), and plain roasted nuts

> Refer to the previous question. Suppose that the car dealer wanted to find values for A and B that minimized the maximum absolute deviation between the actual and estimated selling price for each car. What values of A and B achieve this objective? Data

> Read the feature at the end of section 7.1 in this chapter titled “Balancing Objectives for Enlightened Self-Interest.” What objectives were the real estate developers in this article considering in their plans for the Coal Bank Ridge development? Descri

> A car dealer specializing in late model used cars collected the following data on the selling price and mileage of five cars of the same make and model year at an auto auction: Because there seems to be a strong relationship between mileage and price, t

> KPS Communications is planning to bring wireless Internet access to the town of Ames, Iowa. Using a geographic information system, KPS has divided Ames into the following 5 by 5 grid. The values in each block of the grid indicate the expected annual reve

> A major city in the northeast wants to establish a central transportation station from which visitors can ride buses to four historic landmarks. The city is arranged in a grid, or block, structure with equally spaced streets running north and south and e

> A trust officer at Pond Island Bank needs to determine what percentage of the bank’s investable funds to place in each of following investments. The Yield column represents each investment’s annual yield. The Maturity

> A paper recycling company converts newspaper, mixed paper, white office paper, and cardboard into pulp for newsprint, packaging paper, and print-stock quality paper. The recycler is currently trying to determine the best way of filling an order for 500 t

> The marketing manager for Glissen Paint is working on the weekly sales and marketing plan for the firm’s industrial and contractor sales staff. Glissen’s sales representatives contact two types of customers: existing customers and new customers. Each con

> A private foundation has offered $3 million to allocate to cities to help fund programs that aid the homeless. Grant proposals were received from cities A, B, and C seeking assistance of $750,000, $1.2 million, and $2.5 million, respectively. In the gran

> The Chick’n-Pick’n fast-food chain is considering how to expand its operations. Three types of retail outlets are possible: a lunch counter operation designed for office buildings in downtown areas, an eat-in operation

> The United States Department of Agriculture (USDA) is responsible for managing and administering the national food stamp program. This program provides vouchers to low-income families that can be used in place of cash to purchase food at grocery stores.

> Alaskan Railroad is an independent, stand-alone railroad operation not connected to any other rail service in North America. As a result, rail shipments between Alaska and the rest of North America must be shipped by truck for thousands of miles or loade

> The central Florida high school basketball tournament pits teams from four different counties against one another. The average distance (in miles) between tournament locations in each country is given in the following table. Games are officiated by cert

> Is there an optimal solution to a GP or MOLP problem? Explain.

> The Way gate Corporation makes five different types of metal casing for personal computers. The company is in the process of replacing its machinery with three different new models of metal stamping machines: the Robo-I, Robo-II, and Robo-III. The unit

> Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residences in the Blacksburg area. The plant burns three types of coal, which produce steam that d

> The Royal Seas Company runs a three-night cruise to the Caribbean from Port Canaveral. The company wants to run TV ads promoting its cruises to high-income men, high-income women, and retirees. The company has decided to consider airing ads during prime

> The city of Abingdon is determining its tax rate structure for the coming year. The city needs to generate $6 million in tax revenue via taxes of property, sales, prepared food, and utilities. The following table summarizes how much tax revenue would be

> A new Italian restaurant called the Olive Grove is opening in a number of locations in the Memphis area. The marketing manager for these stores has a budget of $150,000 to use in advertising and promotions for the new stores. The manager can run magazine

> The owner of the Weiner-Meyer meat processing plant wants to determine the best blend of meats to use in the next production run of hamburgers. Three sources of meat can be used. The following table summarizes relevant characteristics of these meats: A

> Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys

> Snow removal and disposal are important and expensive activities in Montreal and many northern cities. Although snow can be cleared from streets and sidewalks by plowing and shoveling, in prolonged subfreezing temperatures, the resulting banks of accumul

> The Reeves Corporation wants to assign each of their 13 corporate clients to exactly one of its three salespersons. The estimated annual sales potential (in $1,000,000s) for each of the Clients is summarized in the following table: A reeve wants each

> The CFO for the Shelton Corporation has $1.2 million to allocate to the following budget requests from five departments: Because the total budget requests exceed the available $1.2 million, not all the requests can be satisfied. Suppose the CFO consider

> Refer to the MOLP problem presented in this chapter. The solutions shown in Figures 7.9, 7.10 and 7.11 each result in more than the required amount of one or more types of coal Being produced, as summarized in the following table. a. Formulate an LP m

> What is the difference between an objective function and a goal?

> Enrique Brava is responsible for upgrading the wireless network for his employer. He has identified seven possible locations to install new nodes for the network. Each node can provide service to different regions within his employer’s

> Bowden Transport provides dispatching services for independent truckers who specialize in transporting cars purchased online from the seller to the buyer. At present, there are four cars needing to be picked up and delivered and five trucks in the vicini

> In the Culprits Control Devices workload balancing problem presented in the chapter a successor task could be assigned to the same workstation as an immediate predecessor task. Suppose we change that assumption so that a successor task cannot be assigned

> The following questions refer to the Blue Ridge Hot Tubs example discussed in this chapter. a. Suppose Howe Jones has to purchase a single piece of equipment for $1,000 in order to produce any Aqua-Spas or Hydro-Lexes. How will this affect the formulatio

> In the CRT Technologies project selection example in this chapter, the problem indicates that surplus funds in any year are reappro priated and cannot be carried over to the next year. Suppose this is no longer the case and surplus funds may be carried o

> A blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. Figure 6.42 shows the possible shipping paths between cities

> Snow removal and disposal are important and expensive activities in Montreal and many northern cities. While snow can be cleared from streets and sidewalks by plowing and shoveling, in prolonged subfreezing temperatures, the resulting banks of accumulate

> The following questions refer to the CRT Technologies project selection example presented in this chapter. Formulate a constraint to implement the conditions described in each of the following statements. a. Out of projects 1, 2, 4, and 6, CRT’s manageme

> The Coola ire Company manufactures air conditioners that are sold to five different retail customers across the United States. The company is evaluating its manufacturing and logistics strategy to ensure that it is operating in the most efficient manner

> The emergency services coordinator for Dade County, Tallies DeCampinas, is interested in locating the county’s two ambulances to maximize the number of residents that can be reached within 4 minutes in emergency situations. The county i

> KPS Communications is planning to bring wireless internet access to the town of Ames, Iowa. Using a geographic information system, KPS has divided Ames into the following 5 by 5 grid. The values in each block of the grid indicate the expected annual reve

> Paul Bergey is in charge of loading cargo ships for International Cargo Company (ICC) at the port in Newport News, Virginia. Paul is preparing a loading plan for an ICC freighter destined for Ghana. An agricultural commodities dealer would like to transp

> Darren Restaurants owns and operates several different restaurant chains including Red Snapper and the Olive Grove. The company is considering opening a number of new units in Ohio. There are 10 different sites available for the company to build new rest

> An automobile manufacturer is considering mechanical design changes in one of its top-selling cars to reduce the weight of the car by at least 400 pounds to improve its fuel efficiency. Design engineers have identified 10 changes that could be made in th

> The Mega-Bucks Corporation is planning its production schedule for the next four weeks and is forecasting the following demand for compound X—a key raw material used in its production process: The company currently has no compound X o

> Bavarian Motor Company (BMC) manufacturers cars and SUVs in Europe and ships them to distributors in the United States. Presently, BMC has an inventory of 200 cars and 140 SUVs in Newark, NJ and 300 cars and 180 SUVs in Jacksonville, FL. These vehicles n

> Dan Boyd is a financial planner trying to determine how to invest $100,000 for one of his clients. The cash flows for the five investments under consideration are summarized in the following table: For example, if Dan invests $1 in investment A at the b

> MasterDebt is a national credit card company with thousands of card holders located across the United States. Every day throughout the month, MasterDebt sends out statements to different customers summarizing their charges for the previous month. Custome

> The Clamped Oil Company has a tanker truck that it uses to deliver fuel to customers. The tanker has five different storage compartments with capacities to hold 2,500, 2,000, 1,500, 1,800 and 2,300 gallons, respectively. The company has an order to deliv

> Consider the following optimization problem: a. What is the optimal solution to this LP problem? b. Now suppose that X1 and X2 must be integers. What is the optimal solution? c. What general principle of integer programming is illustrated by this questi

> Clamped Oil purchases crude oil products from suppliers in Texas (TX), Oklahoma (OK), Pennsylvania (PA), and Alabama (AL), from which it refines four end-products: gasoline, kerosene, heating oil, and asphalt. Because of differences in the quality and ch

> GLMH Shipping is a start-up company that plans to offer same-day shipping services between 20 major cities in the United States. In order to provide this service, GLMH needs to build hubs at airports in several of these cities. GLMH wants to select hub l

> Suppose plants 1 and 2 represent different building alternatives for the same site (i.e., only one of these plants can be built). Similarly, suppose plants 4 and 5 represent different building alternatives for another site. a. What additional constraints

> A manufacturer is considering alternatives for building new plants in order to be located closer to three of its primary customers with whom it intends to develop long-term relationships. The net cost of manufacturing and transporting each unit of the pr

> Howe’s Carpet World has just received an order for carpets for a new office building. The order is for 4,000 yards of carpet 4-feet wide, 20,000 yards of carpet 9-feet wide, and 9,000 yards of carpet 12-feet wide. Howie can order two kinds of carpet rol

> Bellows Lumber Yard, Inc. stocks standard length, 25-foot boards, which it cuts to custom lengths to fill individual customer orders. An order has just come in for 5,000 7-foot boards, 1,200 9-foot boards, and 300 11-foot boards. The lumber yard manager

> A real estate developer is planning to build an apartment building specifically for graduate students on a parcel of land adjacent to a major university. Four types of apartments can be included in the building: efficiencies, and one-, two-, or three-bed

> The demand for electricity varies greatly during the day. Because large amounts of electricity cannot be stored economically, electric power companies cannot manufacture electricity and hold it in inventory until it is needed. Instead, power companies mu

> Tropic sun is a leading grower and distributor of fresh citrus products with three large citrus groves scattered around central Florida in the cities of Mt. Dora, Eustis, and Clermont. Tropic sun currently has 275,000 bushels of citrus at the grove in Mt

> A developer of video game software has seven proposals for new games. Unfortunately, the company cannot develop all the proposals because its budget for new projects is limited to $950,000 and it has only 20 programmers to assign to new projects. The fin

> Identify reasonable values for M12 and M22 in the example on quantity discounts presented in section 6-16b of this chapter.

> The teenage daughter of a recently deceased movie star inherited a number of items from her famous father’s estate. Rather than convert these assets to cash immediately, her financial advisor has recommended that she let some of these a

> Radford Castings can produce brake shoes on six different machines. The following table Summary zes the manufacturing costs associated with producing the brake shoes on each Machine along with the available capacity on each machine. If the company has r

> Charles Mc Keown is an acquisitions editor for a college textbook publisher. The file Books.xlsx that accompanies this book contains a list of 151 textbooks that Charles has an opportunity to acquire from another publisher. For each title, the file lists

> Health Care Systems of Florida (HCSF) is planning to build a number of new emergencycare clinics in central Florida. HCSF management has divided a map of the area into seven regions. They want to locate the emergency centers so that all seven regions wil

> A power company is considering how to increase its generating capacity to meet expected demand in its growing service area. Currently, the company has 750 megawatts (MW) of generating capacity but projects it will need the following minimum generating ca

> A manufacturer of industrial motors has identified ten new prospective customers for its products with estimated each customer’s annual sales potential as follows: The company would like to allocate these ten prospective customers to f

> Snookers Restaurant is open from 8:00 am to 10:00 pm daily. Besides the hours they are open for business, workers are needed an hour before opening and an hour after closing for setup and clean-up activities. The restaurant operates with both full-time a

> Bowden Transport provides dispatching services for independent truckers who specialize in transporting cars purchased online from the seller to the buyer. At present, there are four cars needing to be picked up and delivered and five trucks in the vicini

> Joni Wu manages the Gold Rush Casino in New Orleans. She would like to adjust the assortment of gaming machines in the casino to ensure they are operating in the most profitable manner. The following table summarizes the current assortment of gaming mach

> Garden City Beach is a popular summer vacation destination for thousands of people. Each summer, the city hires temporary lifeguards to ensure the safety of the vacationing public. Garden City’s lifeguards are assigned to work five cons

> Ken Stark is an operations analyst for an insurance company in Muncie, Indiana. Over the next 6 weeks the company needs to send 2,028,415 pieces of marketing literature to customers in the following 16 states: In order to coordinate with other marketing

> As shown in Figure 6.1, the feasible region for an ILP consists of a relatively small, finite number of points, whereas the feasible region of its LP relaxation consists of an infinite number of points. Why, then, are ILPs so much harder to solve than LP

> As rush coordinator for the Alpha Beta Chi (ABC) sorority, Kim Wong asked each pledge to identify five existing members of ABC whom she would most like to have as a big sister. Kim then asks the pledges to rank order these potential big sisters from 5 do

> Suppose the x’s in the following table indicate locations where fire sprinkler heads need to be installed in an existing building. The s indicates the location of the water source to supply these sprinklers. Assume pipe can only be run

> Draw the network representation of the following network flow problem. What kind of network flow problem is this? MIN: 12X13 16X14 15X15 14X23 13X24 17X25 Subject to: 2 X13 2 X14 2 X15 5 28 2 X23 2 X24 2 X25 5 27 1 X13 1 X23 5 15 1 X14 1 X24 5 15 1

> Draw the network representation of the following network flow problem. MIN: 1 7X12 1 6X14 1 3X23 1 4X24 1 5X32 1 9X43 1 8X52 1 5X54 Subject to: 2X12 2 X14 5 2 5 1 X12 1 X52 1 X32 2 X23 2 X24 5 1 4 2 X32 1 X23 1 X43 5 1 8 1 X14 1 X24 1 X54 2 X43 5 1

> Consider the generalized transportation problem shown in Figure 5.35. How can this problem be transformed into an equivalent transportation problem? Draw the network for the equivalent problem.

> Consider the revised Coal Bank Hollow recycling problem discussed in Section 5-5d of this chapter. We said that it is safest to assume the supply in a generalized network flow problem is capable of meeting the demand (until Solver proves otherwise). a. S

> Refer to question 6. Suppose that service at the drive-in window is provided at a rate of 40 customers per hour and follows an exponential distribution. a. What is the expected service time per customer? b. Use equation 13.2 to determine the probability

> The manager of catering services for the Roan oker Hotel has a problem. The banquet hall at the hotel is booked each evening during the coming week for groups who have reserved the following numbers of tables: The hotel has 500 tablecloths that can be u

> A building contractor is designing the ductwork for the heating and air conditioning system in a new, single-story medical building. Figure 5.45 summarizes the possible connections between the primary air handling unit (node 1) and the various air outlet

> The U.S. Department of Transportation (DOT) is planning to build a new interstate to run from Detroit, Michigan, to Charleston, South Carolina. A number of different routes have been proposed and are summarized in Figure 5.44, where node 1 represents Det

> A new airport being built will have three terminals and two baggage pickup areas. An automated baggage delivery system has been designed to transport the baggage from each terminal to the two baggage pickup areas. This system is depicted graphically in F

> The Britt’s & Estragon company manufactures small engines at three different plants. From the plants, the engines are transported to two different warehouse facilities before being distributed to three wholesale distributors. The pe

> Refer to the equipment replacement problem discussed in Section 5-3 of this chapter. In addition to the lease costs described for the problem, suppose that it costs Compu-Train $2,000 extra in labor costs whenever the company replaces their existing comp

> E-mail messages sent over the Internet are broken up into electronic packets that may take a variety of different paths to reach their destination where the original message is reassembled. Suppose the nodes in the graph shown in Figure 5.42 represent a

> Alaskan Railroad is an independent, stand-alone railroad operation not connected to any other rail service in North America. As a result, rail shipments between Alaska and the rest of North America must be shipped by truck for thousands of miles or loade

> Telephone calls for the Yak Line, a discount long distance carrier, are routed through a variety of switching devices that interconnect various network hubs in different cities. The maximum number of calls that can be handled by each segment of their net

> Joe Jones wants to establish a construction fund (or sinking fund) to pay for a new bowling alley he is having built. Construction of the bowling alley is expected to take 6 months and cost $300,000. Joe’s contract with the construction

> The state of Virginia is one of the largest producers of wood furniture in the United States, with the furniture industry accounting for 50% of value added to wood materials. Over the past 40 years the inventory volume of wood in Virginiaâ€&#1

> Union Express has 60 tons of cargo that needs to be shipped from Boston to Dallas. The shipping capacity on each of the routes Union Express planes fly each night is shown in the following table Will Union Express be able to move all 60 tons from Boston

> A residential moving company needs to move a family from city 1 to city 12 in Figure 5.40 where the numbers on the arcs represent the driving distance in miles between cities. a. Create a spreadsheet model for this problem. b. What is the optimal solut

> Omega Airlines has several nonstop flights between Atlanta and Los Angeles every day. The schedules of these flights are shown in the following table. Omega wants to determine the optimal way of assigning flight crews to these different flights. The com

> The Conch Oil Company needs to transport 30 million barrels of crude oil from a port in Doha, Qatar in the Persian Gulf to three refineries throughout Europe. The refineries are in Rotterdam, Netherlands; Toulon, France; and Palermo, Italy, and they req

> An information systems consultant who lives in Dallas must spend the majority of the month of March onsite with a client in San Diego. Her travel schedule for the month is as follows: The usual round-trip ticket price between Dallas and San Diego is $75

> To use the balance-of-flow rule presented in this chapter, constraints for supply nodes must have negative RHS values. Some LP software packages cannot solve problems in which the constraints have negative RHS values. How could these constraints be modif

> The graph in Figure 5.38 represents various flows that can occur through a sewage treatment plant with the numbers on the arcs representing the maximum flow (in tons of sewage per hour) that can be accommodated. Formulate an LP model to determine the max

> A furniture manufacturer has warehouses in cities represented by nodes 1, 2, and 3 in Figure 5.37. The values on the arcs indicate the per unit shipping costs required to transport living room suites between the various cities. The supply of living room

> The blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. The supply and demand for donated blood is shown in Figure

> A cotton grower in south Georgia produces cotton on farms in Statesboro and Brooklet, ships it to cotton gins in Claxton and Millen where it is processed, and then sends it to distribution centers in Savannah, Perry, and Valdosta where it is sold to cust

> If your home or office is carpeted, there’s a good chance that carpet came from Dalton, Georgia— also known as the “Carpet Capital of the World.” Manufacturers in the Dalton area pro