Question: A paper recycling company converts newspaper, mixed
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 tons of newsprint pulp, 600 tons of packaging paper pulp, and 300 tons of print-stock quality pulp. The following table summarizes the yield for each kind of pulp recovered from each ton of recycled material. 
For instance, a ton of newspaper can be recycled using a technique that yields 0.85 tons of newsprint pulp. Alternatively, a ton of newspaper can be recycled using a technique that yields 0.80 tons of packaging paper. Similarly, a ton of cardboard can be recycled to yield 0.80 tons of newsprint or 0.70 tons of packaging paper pulp. Note that newspaper and cardboard cannot be converted to print-stock pulp using the techniques available to the recycler. As each material is recycled, it also produces a toxic sludge that the recycler must dispose of. The amount of toxic sludge (in pounds) created by processing a ton of each of the raw materials into each of the types of pulp is summarized in the following table. For instance, each ton of newspaper that is processed into newspaper pulp creates 125 pounds of sludge. 
The cost of processing each ton of raw material into the various types of pulp is summarized in the following table along with the amount of each of the four raw materials that can be purchased 
These processing costs include the cost of disposing of sludge. However, the managers of the recycling facility would prefer to minimize the amount of sludge created as well as the total cost of filling the order. a. Formulate an MOLP model for this problem and implement your model in a spreadsheet. b. Determine the best possible value for each objective in the problem. c. Determine the solution that minimizes the maximum percentage deviation from the optimal objective function values. What solution do you obtain? d. Suppose management considers minimizing costs to be twice as important as minimizing the amount of sludge produced. What solution does this suggest?
> A mortgage company owns the following 10 mortgages. Investors will purchase packages of mortgages worth at least $1 million. What is the maximum number of such packages that can be created from this set of mortgages? a. Create a spreadsheet model for th
> World Delivery Service (WDS) specializes in the pick-up and delivery of packages at homes and businesses throughout the United States and around the world. WDS utilizes a fleet of trucks that leave from local depots and make a number of pickup and delive
> Barbara Roberts recently received $30,000 as a small inheritance from a distant relative. She wants to invest the money so as to earn $900 to buy a notebook computer next year when she enters graduate school one year from now. (Barbara plans to use her i
> Sometimes the historical data on returns and variances may be poor predictors of how investments will perform in the future. In this case, the scenario approach to portfolio optimization may be used. Using this technique, we identify several different sc
> Mona Obiekwu wants to invest in the stocks of companies A, B, C, and D, whose annual Returns for the past 13 years are as follows. a. Suppose Muna is completely risk averse. What percentage of her portfolio should be invested in each stock and what wou
> An investor wants to determine the safest way to structure a portfolio from several investments. Investment A produces an average annual return of 14% with a variance of 0.025. Investment B produces an average rate of return of 9% with a variance of 0.01
> The Wiggly Piggly Grocery Company owns and operates numerous grocery stores throughout the state of Florida. It is developing plans to consolidate warehouse operations so that there will be 3 different warehouses that supply stores in 10 different region
> Water is delivered throughout New York City using eight main waterlines that are connected at six pumping stations as shown in Figure 8.43. The numbers on each of the arcs indicates the maximum allowable flow of water through each waterline (in 1,000s of
> “So it’s come down to this,” thought Roger Mellichamp as he looked around at the empty Styrofoam coffee cups and papers littering his office. When he accepted the job of campaign manager for his long-
> Beth Dale is the Director of Development for a nonprofit organization that depends largely on charitable gifts for its operations. Beth needs to assign four different staff people to make trips to call on four possible donors. Only one staff person can c
> Consider an optimization problem with two variables and the constraints X1 # 5, X2 # 5 where both X1 and X2 are nonnegative. a. Sketch the feasible region for this problem. b. Sketch level curves of a nonlinear objective for this problem that would have
> The Heat-Aire Company has two plants that produce identical heat pump units. However, production costs at the two differ due to the technology and labor used at each plant. The total costs of production at the plants depend on the quantity produced, and
> An air-ambulance service in Colorado is interested in keeping its helicopter in a central location that would minimize the flight distance to four major ski resorts. An X-Y grid was laid over a map of the area to determine the following latitude and long
> The Rigger Corporation is a Seattle-based R&D company that recently developed a new type of fiber substrate that is waterproof and resists dirt. Several carpet manufacturers in northeast Georgia want to use Rugger as their sole supplier for this new
> The Arctic Oil Company has recently drilled two new wells in a remote area of Alaska. The company is planning to install a pipeline to carry the oil from the two new wells to a transportation and refining (T&R) center. The locations of the oil wells
> A pharmaceutical company is hiring five new salespeople to expand its sales in a western state. Pharmaceutical sales representatives do not sell directly to doctors because doctors do not purchase and distribute drugs. However, doctors do write prescript
> A new mother wants to establish a college education fund for her newborn child. She wants this fund to be worth $100,000 in 18 years. a. If she invests $75 per month, what is the minimum rate of return she would need to earn on her investment? Assume mon
> Carnival Confections, Inc. produces two popular southern food items, pork rinds and fried peanuts, which it sells at a local recreation area on weekends. The owners of the business have estimated their profit function on these items to be: Note that p i
> Howie Jones, owner of Blue Ridge Hot Tubs, is facing a new problem. Although sale of the two hot tubs manufactured by his company (Aqua-Spas and Hydro-Luxes) have been brisk, the company is not earning the level of profits that Howie wants to achieve. Ha
> The summer before completing his MBA, Noah Franklin finally decided to take the trip to Europe that he had always dreamed about. However, given his limited bank account, he knows he will have to plan and budget wisely in order to go everywhere and see ev
> Kan Nutimbo’s family has been planning a visit to a major theme park in Florida. As the family wants to make the most of their time at the park, Kwane has collected data (in the file ParkData.xlsx accompanying this book) that includes estimated walking
> The Radford hardware store expects to sell 1,500 electric garbage disposal units in the coming year. Demand for this product is fairly stable over the year. It costs $20 to place an order for these units and the company assumes a 20% annual holding cost
> In describing the NLP solution strategy summarized in Figure 8.2, we noted that the fastest improvement in the objective function is obtained by moving from point A in a direction that is perpendicular to the level curve of the objective function. Howeve
> Super City is a large retailer of electronics and appliances. The store sells three different models of TVs that are ordered from different manufacturers. The demands, costs, and storage requirements for each model are summarized in the following table:
> The United Delivery Service (UDS) has four vehicles that it uses to make deliveries from its depot to 36 locations in and around Moscow, Idaho. The travel times between each of the delivery locations is summarized in the file UDSData.xlsx that accompanie
> The file InvestmentData.xlsx that accompanies this book contains data on the average returns and covariance’s for 15 different mutual funds. Use this data to answer the following questions: a. Create the efficient frontier associated with this collection
> Lax Rex is an aspiring rock band composed of college friends based in Raleigh, NC. They are planning a short tour that will take them to five other college towns throughout the MidAtlantic region over a 10-day period. The distances between each of the ci
> Vijay Bashwani is organizing a charity golf tournament where teams of four players will play in a captain’s choice format. The handicaps of the 40 players who have registered for the tournament are summarized in the following table. Vij
> Suppose a gift shop in Myrtle Beach has an annual demand for 15,000 units for a souvenir kitchen magnet that it buys for $0.50 per unit. Assume it costs $10 to place an order and the inventory carrying cost is 25% of the item’s unit cost. Use Solver to d
> In the insurance problem discussed in section 8-8 of this chapter, suppose that Thom is confident that he can invest his money to earn a 15% annual rate of return compound quarterly. Assuming a fixed 15% return, suppose he now wants to determine the mini
> The yield of a bond is the interest rate that makes the present value of its cash flows equal to its selling price. Assume a bond can be purchased for $975 and generates the following cash flows: Use Solver to determine the yield for this bond. (Hint: I
> Refer to the insurance problem faced by Thom Pearlman discussed in section 8-8 of this chapter. Let bi represent the balance in his investment at the beginning of year i and let represent the annual interest rate. a. What is the objective function for t
> A traveler was recently stranded in her car in a snowy blizzard in Wyoming. Unable to drive any farther, the stranded motorist used her cell phone to dial 911 to call for help. Because the caller was unsure of her exact location, it was impossible for th
> Can the GRG algorithm be used to solve LP problems? If so, will it always identify a corner point of the feasible region as the optimal solution (as does the simplex method)?
> It has been suggested that one way to solve MOLP problems is to create a composite objective function as a linear combination of all the objectives in the problem. For example, in the previous problem, we might weight the first objective by 0.75 and the
> Consider the following MOLP: a. Graph the feasible region for this problem. b. Calculate the value of each objective at each extreme point. c. What feasible points in this problem are Pareto optimal?
> Suppose that the first goal in a GP problem is to make 2X1 1 5X2 approximately equal to 25. a. Using the deviational variables d1 2 and d1 1, what constraint can be used to express this goal? b. If we obtain a solution where X1 5 4 and X2 5 3, what value
> Refer to the MOLP example presented in this chapter. a. What weights could be used to generate the solution at X1 5 2.5, X2 5 4.5? b. What weights could be used to generate the solution at X1 5 4.0, X2 5 3.0? c. What weights could be used to generate t
> In 2005, Hurricane Katrina decimated the gulf coast of the United States between Mobile, Alabama and New Orleans, Louisiana. The aftermath of this storm left the city of New Orleans flooded, both with water and human victims of the storm. Responding to t
> In 2020, a pandemic swept across the globe killing more than 1 million people and infecting over 100 million more. Responding to this medical and economic disaster was a nightmare and presented governmental and medical decision makers with a number of ex
> A job in a machine shop must undergo five operations—A, B, C, D, and E. Each operation can be performed on either of two machines. The following table summarizes the time required for each machine to perform each operation: Formulate a
> 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
> 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
> A company manufactures three products: A, B, and C. The company currently has an order for 3 units of product A, 7 units of product B, and 4 units of product C. There is no inventory for any of these products. All three products require special processin
> 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.
