Question: Newsome Construction is considering erecting three

> By the time you are reading this, the 2016 NFL season will have finished, and the results should be available at www.pro-football-reference.com/years/ 2016/games.htm. Do whatever it takes to get the data into Excel in the format of this example. Then, us

> The file P07_31.xlsx contains scores on all of the regular-season games in the NBA for the 2015–2016 basketball season. Use the same procedure as in Example 7.8 to rate the teams. Then sort the teams based on the ratings. Do these ratings appear to be ap

> Carry out the suggestion in Modeling Issue 2 for the 2015 NFL season. That is, use a weighted sum of squared prediction errors, where the weight on any game played k weeks ago is 0.95k. You can assume that the ratings are being made right after the final

> In the pricing model with the constant elasticity demand function, the assumption is that all units demanded are sold. Suppose the company has the capacity to produce only 200 units. If demand is less than capacity, all of demand is sold. If demand is gr

> Carry out the suggestion in Modeling Issue 3. That is, find the ratings of the 2015 NFL teams using the sum of absolute prediction errors as the criterion to minimize. Discuss any differences in ratings from this method and the method.

> The file P07_28.xlsx lists the scores of all NFL games played during the 2014 season. Use this data set to rank the NFL teams from best to worst.

> Modify the warehouse location model as suggested in Modeling Issue 2. Specifically, assume that the same four customers have the same annual shipments, but now, there are only two possible warehouse locations, each with distances to the various customers

> The IRR is the discount rate r that makes a project have an NPV of $0. You can find IRR in Excel with the built-in IRR function, using the syntax =IRR(range of cash flows). However, it can be tricky. In fact, if the IRR is not near 10%, this function mig

> Use SolverTable in the warehouse location model to see the effect on the optimal solution of moving one customer farther and farther away from the others. Specifically, let customer 1’s coordinates be of the form (5c, 10c), where the factor c is allowed

> Modify the warehouse location model so that customers always travel in horizontal or vertical directions. For example, this means that if a customer’s coordinates are (5, 10) and a warehouse is located at (7, 7), then the traveling distance is |5 – 7| +

> Modify the warehouse location model so that there is an extra customer. This customer has 250 shipments per year. Try placing this new customer at various locations. For example, try placing the customer way up to the right, or way down to the left, or n

> We implied that each of the five observations was from one period of time, such as a particular week. Suppose instead that each is an average over several weeks. For example, the 4.7 million exposures corresponding to one ad might really be an average ov

> The advertising response function is only one of several nonlinear functions that could be used to get the same “increasing at a decreasing rate” behavior. Another possibility is the function f (n) = anb, where a and b are again constants to be determine

> In the solution to the advertising selection model, we indicated that the women 36 to 55 group is a bottleneck in the sense that the company needs to spend a lot more than it would otherwise have spent to meet the constraint for this group. Use SolverTab

> The preceding problem indicates how fewer alternatives can cause total cost to increase. This problem indicates the opposite. Starting with the solution to the advertising selection problem in Example 7.6, add a new show, “The View,” which appeals primar

> One demand function is linear and the other is called a constant elasticity demand function. Using data tables, show that the price elasticity in the linear demand function is not constant in price, and show that the price elasticity is constant in the c

> Starting with the solution to the advertising selection problem, suppose the company, for whatever reason, cannot place ads on “SportsCenter.” Make the appropriate changes in the model and rerun Solver. Comment on the changes to the decision variable cel

> In judging the fit of the estimated response function, you could use MAE (mean absolute error) instead of RMSE. MAE is the average of the absolute prediction errors. a. When you run Solver with MAE as your objective, do you get approximately the same est

> The file contains a template for a car loan. Specifically, once values are entered in the blue cells, you need to enter formulas in the gray cells to calculate the amount financed, the monthly payment (assuming that monthly payments stay the same through

> The best-fitting advertising response function fits the observed data. This is because we chose the observed data to fall close to a curve of the form. See what happens when one of the observed points is an outlier—that is, it doesn’t fit the pattern of

> In estimating the advertising response function, we indicated that the sum of squared prediction errors or RMSE could be used as the objective, and we used RMSE. Try using the sum of squared prediction errors instead. Does Solver find the same solution a

> Continuing the previous problem (the model in part a) one step further, assume that shirts and ties are also complementary. Specifically, assume that each time a shirt is purchased (and is not accompanied by a suit purchase), 1.3 ties, on average and reg

> In the complementary-product pricing model in Example 7.3, we have assumed that the profit per unit from shirts and ties is given. Presumably this is because the prices of these products have already been set. Change the model so that the company must de

> Continuing Problem 6, suppose the company is selling in the United States, the United Kingdom, and Japan. Assume the unit production cost is $50, and the exchange rates are 1.22 ($/£) and 0.00965 ($/¥). Each country has its own constant elasticity demand

> In the electricity pricing model in Example 7.4, the demand functions have positive and negative coefficients of prices. The negative coefficients indicate that as the price of a product increases, demand for that product decreases. The positive coeffici

> In the electricity pricing model, we assumed that the capacity level is a decision variable. Assume now that capacity has already been set at 0.700 million of mWh. (Note that the cost of capacity is now a sunk cost, so it is irrelevant to the decision pr

> In the complementary-product pricing model, the SolverTable results in Figure 7.21 indicate that the company can sometimes increase overall profit by selling suits below cost. How far might this behavior continue? Answer by extending the SolverTable to l

> Two points on the demand curve were given: a. Suppose three additional points are estimated by Madison: (1) demand of 460 when price is $65, (2) demand of 355 when price is $75, and (3) demand of 275 when price is $85. With these new points and the origi

> Ten different types of brownies are sold. You are thinking of developing a new brownie for sale. Brownies are rated on the basis of five qualities: price, chocolate flavor, chewiness, sweetness, and ease of preparation. You want to group the 10 brownies

> A large U.S. drug company, Pharmco, has 100 million yen coming due in one year. Currently the yen is worth $0.01. Because the value of the yen in U.S. dollars in one year is unknown, the value of this 100 million yen in U.S. dollars is highly uncertain.

> An insurance company has hired you to determine the number of sales divisions into which the country should be divided. Each division will need a president, a vice president, and a divisional staff. The time needed to call on a client will depend on the

> Suppose that you want to divide a state containing 12 cities into five congressional districts. How might you use IP to assign cities to districts?

> Based on McBride and Zufryden (1988). A company is trying to determine which of five possible products to include in its product line. The fixed cost of producing each product and the unit profit for each product are listed in the file P06_96.xlsx. There

> You are moving away from Bloomington and need to load a truck. The items that will go on the truck must all be packed in boxes. The size (in cubic feet) of each item and each available box are listed in the file P06_95.xlsx. For example, the first item r

> Specialty Software is considering 10 projects. The years each project will be developed, the number of programmers needed each year for each project, and the revenue (exclusive of labor costs) from each project are listed in the file P06_94.xlsx. For exa

> This problem is based on Motorola’s online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the n

> The file P06_92.xlsx lists the distances between 21 U.S. cities. You want to locate liver transplant centers in a subset of these 21 cities. a. Suppose you plan to build four liver transplant centers and your goal is to minimize the maximum distance a pe

> You are scheduling company interviews at the annual university career fair. Five interview rooms are available. Interviews are conducted from 9 a.m. to 5 p.m. Each company wants all of its interviews conducted in a single room. The time preferences for t

> A medical supply company has customers in eight cities. It is trying to decide how many salespeople it needs to service these customers. Each salesperson needs to be located in one of the eight cities and needs to be assigned to a subset of the customers

> Make up an example, as described, with 20 possible investments. However, do it so the ROIs are in a very tight range, such as from 12% to 13%. Then use Solver to find the optimal solution when the Solver Integer Optimality setting is 5%, and record the s

> The file contains the cumulative number of bits (in trillions) of DRAM (a type of computer memory) produced and the price per bit (in thousandths of a cent). a. Fit a power curve that can be used to show how price per bit drops with increased production.

> Sam is in his final year of college and is trying to schedule his courses for the year. He has narrowed his search to 16 courses, each of which is offered in at least one time slot (out of a possible five time slots) in each semester. The file P06_89.xls

> Based on Angel et al. (2003). A fertilizer company is trying to determine the cheapest fertilizer mix that provides desired amounts of nutrients. The mix is made by combining the following fertilizers: SSA, SPO, GUR, TSP, KCI, FERT, and SPF. The mix cann

> Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succ

> State University is scheduling 24 sections of a large computer skills course in the Fall semester. There are eight time slots for these sections, four on Monday/ Wednesday (MW) and four on Tuesday/Thursday (TR). In each time slot, three sections are sche

> Based on Spencer et al. (1990). When you lease 800 phone numbers from AT&T for telemarketing, AT&T uses an optimization model to tell you where you should locate calling centers to minimize your operating costs over a 10-year horizon. To illustrate the m

> It is currently the beginning of year 1. Gotham City is trying to sell municipal bonds to support improvements in recreational facilities and highways. The face values of the bonds and the due dates at which principal comes due are listed in the file P06

> A county is going to build two hospitals. There are nine cities in which the hospitals can be built. The number of hospital visits per year made by people in each city and the x-y coordinates of each city are listed in the file P06_83.xlsx. The county’s

> Four trucks are available to deliver milk to five grocery stores. The capacity and daily operating cost of each truck are shown in the file P06_82xlsx. The demand of each grocery store can be supplied by only one truck, but a truck can deliver to more th

> Based on Muckstadt and Wilson (1968). PSI believes it will need the amounts of generating capacity (in millions of kwh) shown in the file P06_80.xlsx during the next five years. The company has a choice of building (and then operating) power plants with

> Suppose the demand (in thousands) for a toaster is given by 100p22, where p is the price in dollars charged for the toaster. a. If the variable cost of producing a toaster is $10, what price maximizes profit? b. The elasticity of demand is defined as the

> As the Quality Sweaters problem is now modeled, if all inputs remain fixed except for the number mailed, profit will increase indefinitely as the number mailed increases. This hardly seems realistic—the company could become infinitely rich. Discuss reali

> Expand and then solve the capital budgeting model so that 20 investments are now possible. You can make up the data on cash requirements, NPVs, and the budget, but use the following guidelines: ■ The cash requirements and NPVs for the various investments

> Arthur Ross, Inc., must complete many corporate tax returns during the period February 15 to April 15. This year, the company must begin and complete the five jobs shown in the file P06_79.xlsx during this eight-week period. Arthur Ross employs four full

> Based on Eaton et al. The city of Springfield has been divided into eight districts. The time (in minutes) it takes an ambulance to travel from one district to another is shown in the file. This file also lists the populations of the districts. Suppose S

> On Monday morning, you have $5000 in cash on hand. For the next seven days, the following cash requirements must be met: Monday, $5000; Tuesday, $6000; Wednesday, $9000; Thursday, $2000; Friday, $7000; Saturday, $2000; Sunday, $3000. At the beginning of

> Based on Efroymson and Ray (1966). Stonecutters is a new bakery chain that sells bread to customers throughout the state of Indiana. Stonecutters is considering building bakeries in three locations: Evansville, Indianapolis, and South Bend. Each bakery c

> Indiana University’s Business School has two rooms that seat 50 students, one room that seats 100 students, and one room that seats 150 students. Classes are held five hours a day. At present, the four types of requests for rooms are listed in the file P

> Based on Bean et al. (1988). Simon’s Mall has 9000 square feet of space to rent and wants to determine the types of stores that should occupy the mall. The minimum number and maximum number of each type of store (along with the square footage of each typ

> Cousin Bruzie of radio station WABC schedules radio commercials in 60-second blocks. This hour, the station has sold time for commercials of 15, 16, 20, 25, 30, 35, 40, and 50 seconds. Determine the minimum number of 60-second blocks of commercials that

> Suppose you own 15 bronze coins worth a total of $150, 12 silver coins worth a total of $160, and 8 gold coins worth a total of $170. Develop a linear integer model to find a combination of coins worth exactly $110.

> Based on Fitzsimmons and Allen (1983). The State of Texas frequently audits companies doing business in Texas. Because these companies often have headquarters located outside the state, auditors must be sent to out-of-state locations. Each year, auditors

> You are thinking of starting Peaco, which will produce Peakbabies, a product that competeswith Ty’s Beanie Babies. In year 0 (right now), you will incur costs of $4 million to build a plant. In year 1, you expect to sell 80,000 Peakbabies for a unit pric

> Based on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the number of units produced, the only production cost during a shift is a setup cost. It costs $8000 to run the day shift and $6000 to run the night shift.

> Change the capital budgeting model so that 80% of each cost in row 5 is incurred right now, at the beginning of year 1, and the other 20% is incurred a year from now, at the beginning of year 2. You can assume that the NPVs don’t change. The available bu

> Based on Boykin (1985). Thompson Chemicals produces 359 million pounds of the chemical maleic anhydride annually. A total of four reactors are available to produce maleic anhydride. Each reactor can be run on one of three settings. The cost (in thousands

> Based on Westerberg, Bjorklund, and Hultman (1977). Newcor’s steel mill has received an order for 25 tons of steel. The steel must be 5% carbon and 6% molybdenum by weight. The steel is manufactured by combining three types of metal: steel ingots, scrap

> Based on Liggett (1973). A court decision has stated that the enrollment of each high school in Metropolis must be at least 20% black. The numbers of black students and white students in each of the city’s five school districts are listed. The distance (

> Spencer Electric ships 17,000 capacitors per month to its customers. The capacitors can be produced at three different plants. The production capacity, fixed monthly cost of operation, and variable cost of producing a capacitor at each plant are given in

> At Blair General Hospital, six types of surgical operations are performed. The types of operations each surgeon is qualified to perform (indicated by an X) are listed in the file P06_65.xlsx. Suppose that surgeons 1 and 2 dislike each other and cannot be

> State University must purchase 1200 computers from three vendors. Vendor 1 charges $250 per computer plus a total delivery charge of $5000. Vendor 2 charges $300 per computer plus a total delivery charge of $4000. Vendor 3 charges $350 per computer plus

> Based on Walker (1974). The Smalltown Fire Department currently has seven conventional ladder companies and seven alarm boxes. The two closest ladder companies to each alarm box are listed in the file. The town council wants to maximize the number of con

> Eight jobs need to be completed. Each job can be completed on any of six machines, and each machine can complete any number of jobs. If a machine is assigned to at least one job, the setup time listed in the file is required. (All times are in hours.) Th

> Suppose you are borrowing $25,000 and making monthly payments with 1% interest. Show that the monthly payments should equal $556.11. The key relationships are that for any month t (Ending month t balance) = (Ending month t - 1 balance) - ((Monthly paymen

> Bertallo Classic produces tomato sauce at five different plants. The tomato sauce is then shipped to one of three warehouses, where it is stored until it is shipped to one of the company’s four customers. The following inputs for the problem are given in

> Ford has four automobile plants. Each is capable of producing the Focus, Mustang, or Taurus, but it can produce only one of these cars. The fixed cost of operating each plant for a year and the variable cost of producing a car of each type at each plant

> As it currently stands, investment 7 in the capital budgeting model has the lowest ROI. Keeping this same ROI, can you change the cash requirement and NPV for investment 7 so that it is selected in the optimal solution? Does this lead to any general insi

> At a machine tool plant, five jobs must be completed each day. The time it takes to do each job depends on the machine used to do the job. If a machine is used at all, a setup time is required. The relevant times (in minutes) are given in the file P06_59

> During the next five periods, the demands listed in the file must be met on time. At the beginning of period 1, the inventory level is 0. During each period when production occurs, a setup cost of $10,000 and a per-unit production cost of $45 are incurre

> Eastinghouse sells air conditioners. The annual demand for air conditioners in each region of the country is as follows: East, 100,000; South, 150,000; Midwest, 110,000; and West, 90,000. Eastinghouse is considering building its air conditioners in four

> Toshovo Computer owns four production plants at which computer workstations are produced. The company can sell up to 40,000 computers per year at a price of $1500 per computer. For each plant, the production capacity, the production cost per computer, an

> McPherson Publishers is considering publishing five textbooks. The maximum number of copies of each textbook that can be sold, the variable cost of producing each textbook, the selling price of each textbook, and the fixed cost of a production run for ea

> Consider the Pigskin example. Find Pigskin’s optimal production policy if, in addition to the given production and holding costs, there is a fixed cost of $50,000 during any month in which there is positive production. Assume now that storage capacity is

> A product can be produced on four different machines. Each machine has a fixed setup cost, variable production cost per unit processed, and a production capacity, given in the file P06_53.xlsx. A total of 2000 units of the product must be produced. Deter

> You are entering the widget business. It costs $500,000, payable in year 1, to develop a prototype. This cost can be depreciated on a straight-line basis during years 1 to 5. Each widget sells for $40 and incurs a variable cost of $20. During year 1, the

> Avion Computer produces two types of computers: Pear computers and Apricot computers. The relevant data are given in the file P06_52.xlsx. The equipment cost is a fixed cost that is incurred if any of this type of computer is produced. A total of 4000 ch

> The TightBond company produces three types of glue on two different production lines. Each line can be used by up to 20 workers at a time. Workers are paid $500 per week on production line 1 and $900 per week on production line 2. For a week of productio

> A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 15,000 units per week. The weekly fixed cost of keeping each warehouse open is $60,000 for New York, $50,000 for Los Angeles,

> In the capital budgeting model, investment 4 is tied for the largest ROI, but it is not selected in the optimal solution. How much NPV will be lost if Tatham is forced to select investment 4? Answer by solving a suitably modified model.

> A manufacturer can sell product 1 at a profit of $20 per unit and product 2 at a profit of $40 per unit. Three units of raw material are needed to manufacture one unit of product 1, and six units of raw material are needed to manufacture one unit of prod

> Because of excessive pollution on the Momiss River, the state of Momiss is going to build some pollution control stations. Three sites are under consideration. Momiss is interested in controlling the pollution levels of two pollutants. The state legislat

> Based on Sonderman and Abrahamson (1985). In treating a brain tumor with radiation, physicians want the maximum amount of radiation possible to bombard the tissue containing the tumors. The constraint is, however, that there is a maximum amount of radiat

> The Cubs are trying to determine which of the following free-agent pitchers should be signed: Rick Sutcliffe (RS), Bruce Sutter (BS), Dennis Eckersley (DE), Steve Trout (ST), or Tim Stoddard (TS). (Feel free to substitute your own set of players for thes

> Based on Bean et al. (1987). Boris Milkem’s firm owns six assets. The expected selling price (in millions of dollars) for each asset is given in the file. For example, if asset 1 is sold in year 2, the firm receives $20 million. To maintain a regular cas

> To graduate from Southeastern University with a major in operations research (OR), a student must complete at least three math courses, at least three OR courses, and at least two computer courses. Some courses can be used to fulfill more than one requir

> The payback of a project is the number of years it takes before the project’s total cash flow is positive. Payback ignores the time value of money. It is interesting, however, to see how differing assumptions on project growth impact payback. Suppose, fo

> Coach Night is trying to choose the starting lineup for the basketball team. The team consists of seven players who have been rated on a scale of 1 (poor) to 3 (excellent) according to their ball handling, shooting, rebounding, and defensive abilities. T

> NASA must determine how many of three types of objects to bring on board the space shuttle. The weight and benefit of each of the items. If the space shuttle can carry up to 2000 pounds of items 1 through 3, how many of each item should be taken on the s

> You are moving from New Jersey to Indiana and have rented a truck that can haul up to 1100 cubic feet of furniture. The volume and value of each item you are considering moving on the truck. Which items should you bring to Indiana?

> You are given a group of possible investment projects for your company’s capital. For each project, you are given the NPV the project would add to the firm, as well as the cash outflow required by each project during each year. Given the information in t