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practical management science
Practical Management Science 5th Edition Wayne L. Winston, Christian Albright - Solutions
Based on Hansen and Wendell (1982). During the month of July, Pittsburgh resident Bill Fly must make four round-trip flights between Pittsburgh and Chicago. The dates of the trips are shown in the file P05_64.xlsx. Bill must purchase four round-trip tickets. Without a discounted fare, a round-trip
Powerhouse produces capacitors at three locations: Los Angeles, Chicago, and New York. Capacitors are shipped from these locations to public utilities in five regions of the country: northeast (NE), northwest (NW), midwest (MW), southeast (SE), and southwest (SW). The cost of producing and shipping
Delko is considering hiring people for four types of jobs. The company would like to hire the number of people listed in the file P05_62.xlsx for each type of job. Delko can hire four types of people. Each type is qualified to perform two types of jobs, as shown in this same file. A total of 20
At the beginning of year 1, a new machine must be purchased. The cost of maintaining a machine, depending on its age, is given in the file P05_61.xlsx. The cost of purchasing a machine at the beginning of each year is given in this same file. There is no trade-in value when a machine is replaced.
Suppose it costs $20,000 to purchase a new car. The annual operating cost and resale value of a used car are shown in the file P05_60.xlsx. Assume that you presently have a new car. Determine a replacement policy that minimizes your net costs of owning and operating a car for the next six years.
It costs $300 to buy a lawn mower from a lawn supply store. Assume that you can keep a lawn mower for at most five years and that the estimated maintenance cost each year of operation is as follows: year 1, $90; year 2, $135; year 3, $175; year 4, $200; year 5, $250. You have just purchased a new
Edsel Motors produces cars in Detroit and Dallas. The Detroit plant can produce up to 8500 cars, and the Dallas plant can produce up to 4000 cars. Producing a car costs $2000 in Detroit and $1800 in Dallas. Cars must be shipped to 12 cities. The costs of shipping a car from each plant to each city
Nash Auto has two plants, two warehouses, and three customers. The plants are in Detroit and Atlanta, the warehouses are in Denver and New York, and the customers are in Los Angeles, Chicago, and Philadelphia. Cars are produced at plants, then shipped to ware-houses, and finally shipped to
Sunco Oil produces oil at two wells. Well 1 can produce up to 150,000 barrels per day, and well 2 can produce up to 200,000 barrels per day. It is possible to ship oil directly from the wells to Sunco’s customers in Los Angeles and New York. Alternatively, Sunco could transport oil to the ports
A company manufactures widgets at two factories, one in Memphis and one in Denver. The Memphis factory can produce up to 150 widgets per day, and the Denver factory can produce up to 200 widgets per day. The company are shipped by air to customers in Los Angeles and Boston. The customers in
A company is taking bids on four construction jobs. Three contractors have placed bids on the jobs. Their bids (in thousands of dollars) are given in the file P05_52.xlsx. (A blank indicates that the contractor did not bid on the given job.) Contractor 1 can do only one job, but contractors 2 and 3
Based on Machol (1970). A swimming coach is putting together a relay team for the 400-meter relay. Each swimmer must swim 100 meters of breaststroke, backstroke, butterfly, or freestyle, and each swimmer can swim only one race. The coach believes that each swimmer can attain the times given in the
Five employees are available to perform four jobs. The time it takes each person to perform each job is given in the file P05_50.xlsx. Determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs. (A blank indicates that a person cannot do that
Touche Young has eight auditors. Each can work up to 160 hours during the next month, during which time six projects must be completed. The hours required for each project and the amounts each auditor can be billed for each project are given in the file P05_49.xlsx. Note that more than one auditor
The Amorco Oil Company controls two oil fields. Field 1 can produce up to 20 million barrels of oil per day, and field 2 can produce up to 15 million barrels of oil per day. At field 1, it costs $37.50 to extract and refine a barrel of oil; at field 2 the cost is $41.20. Amorco sells oil to two
The 7th National Bank has two check-processing sites. Site 1 can process 10,000 checks per day, and site 2 can process 6000 checks per day. The bank processes three types of checks: vendor, salary, and personal. The processing cost per check depends on the site, as listed in the file P05_47.xlsx.
The government is auctioning off oil leases at two sites. At each site, 100,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bidding for the oil. Government rules state that no bidder can receive more than 40% of the land being auctioned. Cliff has bid $1000
A school system has 16 bus drivers that must cover 12 bus routes. Each driver can cover at most one route. The driver’s bids for the various routes are listed in the file P05_45.xlsx. Each bid indicates the amount the driver will charge the school system to drive that route. How should the
You are trying to help the MCSCC (Monroe County School Corporation) determine the appropriate high school district for each housing development in Bloomington. For each development, you are given the number of students, the mean family income, the percentage of minorities, and the distance to each
A truck must travel from New York to Los Angeles. As shown in Figure 5.44, several routes are available. The number associated with each arc is the number of gallons of fuel required by the truck to traverse the arc. Determine the route from New York to Los Angeles that uses the minimum amount of
The town of Busville has three school districts. The numbers of black students and white students in each district are shown in the file P05_42.xlsx. The Supreme Court requires the schools in Busville to be racially balanced. Thus, each school must have exactly 300 students, and each school must
One rather unrealistic assumption in the flight-scheduling model is that a given plane can fly two consecutive flights with no downtime. For example, it could fly flight 5903 that gets into Washington, D.C. at time 14 and then fly flight 7555 that leaves Washington, D.C. at time 14. Modify the
In the flight-scheduling model, use SolverTable to examine the effect of increasing both the fixed cost per plane and the overnight cost by the same percentage, assuming that the company owns eight planes. Let this percentage vary from 0% to 50% in increments of 10%. Discuss the changes that occur
In the flight-scheduling model, use SolverTable to examine the effect of decreasing all net revenues by the same percentage, assuming that the company owns six planes. Let this percentage vary from 0% to 50% in increments of 10%. Discuss the changes that occur in the optimal solution.
We illustrated how a machine replacement problem can be modeled as a shortest path problem. This is probably not the approach most people would think of when they first see a machine replacement problem. In fact, most people would probably never think in terms of a network. How would you model the
In the VanBuren machine replacement problem, suppose the company starts with a machine that is eight quarters old at the beginning of the first quarter. Modify the model appropriately, keeping in mind that this initial machine must be sold no more than four quarters from now.
In the VanBuren machine replacement problem, the company’s current policy is to keep a machine at least four quarters but no more than 12 quarters. Suppose instead that the company imposes no upper limit on how long it will keep a machine; its only policy requirement is that a machine must be
In the VanBuren machine replacement problem, we assumed that the maintenance cost and salvage values are linear functions of age. Suppose instead that the maintenance cost increases by 50% each quarter and that the salvage value decreases by 10% each quarter. Rework the model with these
Continuing the previous problem, suppose again that all arcs go in both directions, but suppose Maude’s objective is to find the shortest path from node 1 to node 7 (not node 10). Modify the spreadsheet model appropriately and solve.
In Maude’s shortest path problem, suppose all arcs in the current network from higher-numbered nodes to lower-numbered nodes, such as from node 6 to node 5, are disallowed. Modify the spreadsheet model and find the shortest path from node 1 to node 10. Is it the same as before? Should you have
In Maude’s shortest path problem, suppose all arcs in the network are double-arrowed, that is, Maude can travel along each arc (with the same distance) in either direction. Modify the spreadsheet model appropriately. Is her optimal solution still the same?
Expand the RedBrand two-product spreadsheet model so that there are now three products competing for the arc capacity. You can make up the required input data.
In the original RedBrand problem, we assume a constant arc capacity, the same for all allowable arcs. Modify the model so that each arc has its own arc capacity. You can make up the required arc capacities.
When we (the authors) originally developed the bus route assignment model, we included an arc capacity constraint: Flow #1. After giving this further thought, we deleted this constraint as being redundant. Why could we do this? Specifically, why can’t one or more of the flows found by Solver be
In the optimal solution to the bus route assignment problem, company 2 is assigned to bus routes 6 and 7. Suppose these two routes are far enough apart that it is infeasible for one company to service both of them. Change the model to accommodate this restriction and find the new optimal solution.
In the optimal solution to the machine-to-job assignment problem, jobs 3 and 4 are assigned to different machines. Suppose there is an extra restriction that these jobs must be assigned to the same machine. Change the model to accommodate this restriction and find the new optimal solution.
In the optimal solution to the machine-to-job assignment problem, jobs 1 and 2 are both assigned to machine 4. Suppose there is an extra restriction that jobs 1 and 2 must be assigned to different machines. Change the model to accommodate this restriction and find the new optimal solution.
We modeled the bus route assignment problem with the alternative form of the transportation model (as in Figure 5.8). Model it instead with the standard form (as in Figure 5.3). Discuss the pros and cons of these two approaches for this particular example.Figure 5.3: 17) 21 13
Modify the bus route assignment model, assuming that company 1 decides to place bids on routes 7 and 8 (in addition to its current bids on other routes). The bids on these two routes are $5200 and $3300. Does the optimal solution change?
In the machine-to-job assignment problem, the current capacities of the machines are 1, 2, 1, 2, and 1. If you could increase one of these capacities by 1, which would you increase? Why?
Modify the machine-to-job assignment model under the assumption that only three of the four jobs must be completed. In other words, one of the four jobs does not have to be assigned to any machine. What is the new optimal solution?
One possible solution method for the machine-to-job assignment problem is the following heuristic procedure. Assign the machine to job 1 that completes job 1 quickest. Then assign the machine to job 2 that, among all machines that still have some capacity, completes job 2 quickest. Keep going until
1. Find the optimal March shipment schedule and its total transportation cost for each of the following:a. Cottonb. Polyesterc. Silk2. The company will be opening a silk-making department in the Nigeria mill. Although it will not be completed for several months, a current capacity of 1000 bolts for
In the current blending model, a barrel of any input results in a barrel of output. However, in a real blending problem, there can be losses. Suppose a barrel of input results in only a fraction of a barrel of output. Specifically, each barrel of either crude oil used for gasoline results in only
Owens-Wheat uses two production lines to produce three types of fiberglass mat. The demand requirements (in tons) for each of the next four months are shown in the file P04_115.xlsx. If it were dedicated entirely to the production of one product, a line 1 machine could produce either 20 tons
Rylon Corporation manufactures Brute cologne and Chanelle perfume. The raw material needed to manufacture each type of fragrance can be purchased for $60 per pound. Processing 1 pound of raw material requires 1 hour of laboratory time. Each pound of processed raw material yields 3 ounces of
A large CPA firm currently has 100 junior staff members and 20 partners. In the long run–say, 20 years from now–the firm would like to consist of 130 junior staff members and 20 partners. During a given year, 10% of all partners and 30% of all junior staff members leave the firm. The firm can
Based on Rothstein (1973). The Springfield City Police Department employs 30 police officers. Each officer works five days per week. The crime rate fluctuates with the day of the week, so the number of police officers required each day depends on the day of the week, as follows: Saturday, 28;
Mondo Motorcycles is determining its production schedule for the next four quarters. Demands for motorcycles are forecasted to be 400 in quarter 1; 700 in quarter 2; 500 in quarter 3; and 200 in quarter 4. Mondo incurs four types of costs, as described here:■ It costs Mondo $800 to
The HiTech company produces Blu-Ray disc players. Estimated demands for the next four quarters are 5000, 10,000, 8000, and 2000. At the beginning of quarter 1, HiTech has 60 workers. It costs $2000 to hire a worker and $4000 to fire a worker. Workers are paid $10,000 per quarter plus $80 for each
An oil company produces gasoline from five inputs. The cost, density, viscosity, and sulfur content, and the number of barrels available of each input are listed in the file P04_78.xlsx. Gasoline sells for $72 per barrel. Gasoline can have a density of at most 0.98 units per barrel, a viscosity of
A company produces two products: A and B. Product A sells for $11 per unit and product B sells for $23 per unit. Producing a unit of product A requires two hours on assembly line 1 and one unit of raw material. Producing a unit of product B requires two units of raw material,
Carrington Oil produces gas 1 and gas 2 from two types of crude oil: crude 1 and crude 2. Gas 1 is allowed to contain up to 4% impurities, and gas 2 is allowed to contain up to 3% impurities. Gas 1 sells for $72 per barrel, whereas gas 2 sells for $84 per barrel. Up to 4200
Candy Kane Cosmetics (CKC) produces Leslie Perfume, which requires chemicals and labor. Two production processes are available. Process 1 transforms one unit of labor and two units of chemicals into three ounces of perfume. Process two transforms two units of labor and three units of chemicals into
Based on Heady and Egbert (1964). Walnut Orchard has two farms that grow wheat and corn. Because of differing soil conditions, there are differences in the yields and costs of growing crops on the two farms. The yields and costs are listed in the file P04_67.xlsx. Each farm has 100 acres available
At the beginning of year 1, you have $10,000. Investments A and B are available; their cash flows are shown in the file P04_62.xlsx. Assume that any money not in-vested in A or B earns interest at an annual rate of 3%.a. Determine how to maximize your cash on hand in year 4.b. Use SolverTable to
A furniture company manufactures tables and chairs. A table requires 40 board-feet of wood, and a chair requires 30 board-feet of wood. Wood can be purchased at a cost of $1.50 per board-foot, and 40,000 board-feet of wood are available for purchase. It takes two hours of skilled labor to
Hiland’s Appliances stocks laptops, TVs, refrigerators, microwave ovens, and ranges. These products compete for floor space, tie up different amounts of capital, and have different profit margins. The company has also specified minimum percentages of these products it wants to stock (out of the
Young MBA Erica Cudahy can invest up to $15,000 in stocks and loans. Each dollar invested in stocks yields $0.10 profit, and each dollar invested in a loan yields $0.15 profit. At least 30% of all money invested must be in stocks, and at least $6000 must be in loans. Determine how Erica can
Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 100,000 pounds of grade 9 oranges and 120,000 pounds of grade 6 oranges on hand. The average quality of oranges sold in
You have decided to enter the candy business. You are considering producing two types of candies: Slugger candy and Easy Out candy, both of which consist solely of sugar, nuts, and chocolate. At present, you have in stock 10,000 ounces of sugar, 2000 ounces of nuts, and 3000 ounces of chocolate.
NewAge Pharmaceuticals produces the drug NasaMist from four chemicals. Today, the company must produce 1000 pounds of the drug. The three active ingredients in NasaMist are A, B, and C. By weight, at least 8% of NasaMist must consist of A, at least 4% must consist of B, and at least 2% must consist
During each four-hour period, the Smalltown police force requires the following number of on-duty police officers: eight from midnight to 4 a.m.; seven from 4 a.m. to 8 a.m.; six from 8 a.m. to noon; six from noon to 4 p.m.; five from 4 p.m. to 8 p.m.; and four from 8 p.m. to midnight. Each
A bus company believes that it will need the following numbers of bus drivers during each of the next five years: 60 drivers in year 1; 70 drivers in year 2; 50 drivers in year 3; 65 drivers in year 4; and 75 drivers in year 5. At the beginning of each year, the bus company must decide how
You have been commissioned by Indiana University to evaluate the relative efficiency of four degree-granting units: Business, Education, Arts and Sciences, and Health, Physical Education, and Recreation (HPER). You are given the information in the file P04_44.xlsx. Use DEA to identify all
You have been asked to evaluate the efficiency of the Port Charles Police Department. Three precincts are to be evaluated. The inputs and outputs for each precinct are as follows:■ Input 1 = number of policemen■ Input 2 = number of vehicles used■ Output 1 = number of patrol units responding
The Salem Board of Education wants to evaluate the efficiency of the town’s four elementary schools. The three outputs of the schools are■ Output 1 = average reading score■ Output 2 = average mathematics score■ Output 3 = average self-esteem scoreThe three inputs to the schools are■ Input
Pine Valley Bank has three branches. You have been asked to evaluate the efficiency of each. The following inputs and outputs are to be used for the study:■ Input 1 = labor hours used (hundreds per month)■ Input 2 = space used (in hundreds of square feet)■ Input 3 = supplies used per month
The pension fund model is streamlined, perhaps too much. It does all of the calculations concerning cash flows in row 20. James decides he would like to break these out into several rows of calculations: Beginning cash (for year 1, this is the amount allocated; for other years, it is the unused
In the pension fund model, suppose James has been asked to see how the optimal solution changes if the required payments in years 6 to 15 all increase by the same percentage, where this percentage could be anywhere from 5% to 25%. Use an appropriate one-way SolverTable to help him out, and write a
In the pension fund model, suppose there is a fourth bond, bond 4. Its unit cost in year 1 is $1020, it returns coupons of $70 in years 2 to 5 and a payment of $1070 in year 6. Modify the model to incorporate this extra bond and reoptimize. Does the solution change–that is, should James purchase
In a production process model such as Repco’s, certain inputs make no sense in the usage table (the range B7:D9 of the model). For example, suppose that, in addition to current usages, each unit of drug A requires one unit of drug C. Why does this result in a nonsensical problem? What happens if
We claimed that the Repco model could either con-strain the units produced to be greater than or equal to the units used by production or constrain the units sold to be nonnegative. Modify the model to implement the latter (deleting the former), and verify that you get the same optimal solution.
Suppose there is a fourth drug, drug D, that Repco can produce and sell. Each unit of drug D requires four labor hours, one unit of drug A, and one unit of drug C to produce, and it sells for $150 per unit. Modify the current model to incorporate drug D and re-optimize. If drug D isn’t produced
Run a one-way sensitivity analysis on the optimal solution to the unit selling price of drug A in the Repco model. If this price is high enough, will Repco start selling drug A in addition to producing it? Then run a similar one-way sensitivity analysis on the optimal solution to the price of drug
We warned you about clearing denominators in the quality constraints. This problem illustrates what can happen if you don’t do so.a. Implement the quality constraints as indicated in Inequality (4.3) of the text. Then run Solver with the Simplex LP method. What happens? What if you use the GRG
In Chandler’s blending model, suppose a chemical ingredient called CI is needed by both gasoline and heating oil. At least 3% of every barrel of gasoline must be CI, and at least 5% of every barrel of heating oil must be CI. Suppose that 4% of all crude oil 1 is CI, and that 6% of all crude oil 2
How sensitive is the optimal solution (barrels of each input and output sold and total revenue) to the required quality levels? Answer this by running a two-way SolverTable with these five outputs. You can choose the values of the two quality levels to vary.
Use SolverTable in Chandler’s blending model to see whether, by increasing the selling price of gasoline, you can get an optimal solution that produces only gasoline, no heating oil. Then use SolverTable again to see whether, by increasing the selling price of heating oil, you can get an optimal
In the current no-backlogging problem, Sure Step doesn’t hire any workers and uses almost no overtime. This is evidently because of low demand. Change the demands to 6000, 8000, 5000, and 3000, and re-optimize. Is there now hiring and overtime? With this new demand pattern, explore the trade-off
In the employee scheduling example, suppose that the company can require the employees to work one day of overtime each week on the day immediately following this five-day shift. For example, an employee whose regular shift is Monday to Friday can also be required to work on Saturday. Each employee
Suppose the company has 25 full-time employees and is not allowed to hire or fire any of them. Determine a schedule that maximizes the number of weekend days off received by these employees.
Suppose there are three objectives, not just two: the total advertising cost, the total number of excess exposures to men, and the total number of excess exposures to women. Continuing the approach suggested in the previous problem, how might you proceed? Take it as far as you can, including a
In the dual-objective advertising model, we put a budget constraint on the total advertising cost and then maximized the total number of excess exposures. Do it the opposite way, reversing the roles of the two objectives. That is, model it so that you put a lower limit on the total number of excess
Suppose that General Flakes decides that it shouldn’t place any more than 10 ads on any given show. Modify the (original) advertising model appropriately to incorporate this constraint, and then reoptimize (with integer constraints on the numbers of ads). Finally, run Solver-Table to see how
Suppose, in addition to the shows already listed, General Flakes wants to open the possibility of purchasing ads on the “Good Morning America” show on ABC. Make up any reasonable input data you need to include this possibility in the (original) model, and find the optimal solution.
1. Develop an LP model to determine whether there are any arbitrage opportunities with the spot currency rates given in the file. Note that an arbitrage opportunity could involve several currencies. If there is an arbitrage opportunity, your model should specify the exact set of transactions to
Suppose, as a matter of corporate policy, that General Flakes decides not to advertise on the Rachael Ray show. Modify the original advertising model appropriately and find the new optimal solution. How much has it cost the company to make this policy decision?
1. You should develop an Excel optimization model to find the optimal strategy. This strategy should specify the number of each type of ac-count (0-due, 1-due, 2-due, 3-due) that should receive each contact type (letter, phone call, no contact) in each month. You should also describe the
In addition to the constraints already in the (original) advertising model, suppose General Flakes also wants to obtain at least 180 million exposures to men and at least 160 million exposures to women. Does the current optimal solution satisfy these constraints? If not, modify the model as
1. Dave is not absolutely sure that the "side" constraint of at least as much gas A as gas B is necessary. What is this constraint costing the company? That is, how much more revenue could Jansen earn if this constraint were ignored?2. Dave consults the chemical experts, and they suggest
A graduated payment mortgage (GPM) enables the borrower to have lower payments earlier in the mortgage and increased payments later on. The assumption is the borrower’s income will increase over time so that it will be easier for the borrower to meet all payments. Suppose you borrow $60,000 on a
The Internal Revenue Service (IRS) has determined that during each of the next 12 months it will need the numbers of supercomputers given in the file P04_88.xlsx. To meet these requirements, the IRS rents supercomputers for a period of one, two, or three months. It costs $1000 to rent a
You own a wheat warehouse with a capacity of 20,000 bushels. At the beginning of month 1, you have 6000 bushels of wheat. Each month, wheat can be bought and sold at the prices per bushel listed in the file P04_89.xlsx. The sequence of events during each month is as follows:■ You observe your
A furniture company manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 15,000 board feet of oak and 21,000 board feet of pine are available. A table requires either 17 board feet of oak or 30 board feet of pine, and a chair
George needs help to decide how many grapes to buy, how much money to spend on advertising, how many bottles of wine to sell, and how much profit he can expect to earn over the two-year period. Develop and then solve a spreadsheet LP model to help him. Then use this model to answer the following
Shelby Shelving is a small company that manufactures two types of shelves for grocery stores. Model S is the standard model; model Lx is a heavy-duty version. Shelves are manufactured in three major steps: stamping, forming, and assembly. In the stamping stage, a large machine is used to stamp
A textile company produces shirts and pants. Each shirt requires two square yards of cloth, and each pair of pants requires three square yards of cloth. During the next two months the following demands for shirts and pants must be met (on time): month 1, 1000 shirts and 1500 pairs of pants; month
In a typical production scheduling model like Pigskin’s, if there are no production capacity constraints—the company can produce as much as it needs in any time period—but there are storage capacity constraints and demand must be met on time, is it possible that there will be no feasible
Calculate the amount financed, the monthly payment (assuming that monthly payments stay the same throughout the term of the loan), the total interest paid, and an amortization schedule. For the latter, fill in the entire gray area with formulas, but use IF functions so that blanks appear past the
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