Question: Two points on the demand curve were

> It costs a company $15 to purchase an hour of labor and $20 to purchase an hour of capital. If L hours of labor and K units of capital are available, then 0.075L2/3K1/3 machines can be produced. Suppose the company has $150,000 to purchase labor and capi

> Continuing Problem 3 in a slightly different direction, create a two-way SolverTable where the inputs are the elasticity and the production capacity, and the outputs are the optimal price and the optimal profit. (This actually creates two tables, one for

> If a monopolist produces q units, she can charge 400 - 4q dollars per unit. The variable cost is $60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase

> A company produces widgets at plants 1 and 2. It costs 135x1/2 dollars to produce x units at plant 1 and 260x1/3 dollars to produce x units at plant 2. Each plant can produce up to 1000 units. Each unit produced can be sold for $12. At most 1700 widgets

> Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excel’s

> Suppose the current exchange rate is 115 yen per dollar. We currently have a demand for 50 units of our product when the unit price is 800 yen. The cost of producing and shipping the product to Japan is $6, and the current elasticity of demand is -2.5. F

> Suppose Ford currently sells 250,000 Ford Mustangs annually. The unit cost of a Mustang, including the delivery cost to a dealer, is $16,000. The current Mustang price is $20,000, and the current elasticity of demand for the Mustang is 21.5. a. Determine

> The file contains data on prices of products for several of a chain store’s locations, a discount schedule offered to customers depending on how much they spend, and commission rates of the salespeople at the various stores. Your job is to develop an inv

> Solve the previous problem, but analyze GE instead of Microsoft.

> Given the data in the file Stock Beta.xlsx, estimate the beta (and alpha) for Microsoft (MSFT). Do this for each criterion to obtain a table analogous to that in the top right. What do you conclude about Microsoft?

> In many cases, the portfolio return is at least approximately normally distributed. Then Excel’s NORMDIST function can be used to calculate the probability that the portfolio return is negative. The relevant formula is =NORMDIST(0,mean, stdev,True), wher

> Continuing the previous problem, find the portfolio that achieves an expected monthly return of at least 1% and minimizes portfolio variance. Then use SolverTable to sweep out the efficient frontier. Create a chart of this efficient frontier from your So

> This problem continues using the data from the previous problem. The file includes all of the previous data and contains investment weights in row 3 for creating a portfolio. These fractions are currently all equal to 1/27, but they can be changed to any

> Continuing the previous problem, create a two-way data table similar to the one-way data. This time, however, allow price to vary down a column and allow the capacity to vary across a row. Each cell of the data table should capture the corresponding prof

> The file contains historical monthly returns for 27 companies. For each company, calculate the estimated mean return and the estimated variance of return. Then calculate the estimated correlations between the companies’ returns. Note that “return” here m

> The stocks are all positively correlated. What happens when they are negatively correlated? Answer for each of the following scenarios. In each case, two of the three correlations are the negatives of their original values. Discuss the differences betwee

> In the model, stock 2 is not in the optimal portfolio. Use SolverTable to see whether it ever enters the optimal portfolio as its correlations with stocks 1 and 3 vary. Specifically, use a two-way SolverTable with two inputs, the correlations between sto

> Add a new stock, stock 4, to the model. Assume that the estimated mean and standard deviation of return for stock 4 are 0.125 and 0.175, respectively. Also, assume the correlations between stock 4 and the original three stocks are 0.3, 0.5, and 0.8. Run

> A project does not necessarily have a unique IRR. (Refer to the previous problem for more information on IRR.) Show that a project with the following cash flows has two IRRs: year 1, -$20; year 2, $82; year 3, -$60; year 4, $2.

> For each of the following, answer whether it makes sense to multiply the matrices of the given sizes. In each case where it makes sense, demonstrate an example in Excel, where you can make up the numbers. a. AB, where A is 3 × 4 and B is 4 × 1 b. AB, whe

> The method for rating teams is based on actual and predicted point spreads. This method can be biased if some teams run up the score in a few games. An alternative possibility is to base the ratings only on wins and losses. For each game, you observe whe

> By the time you are reading this, the 2016–2017 NBA season will have finished, and the results should be available at www.basketball-reference.com/leagues/NBA_2017_games.html. Do whatever it takes to get the data into Excel in the format of this example.

> 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

> 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

> Newsome Construction is considering erecting three office buildings. The time (in years) required to complete each of them and the number of workers required to be on the job at all times are shown in the file P06_81.xlsx. After a building is completed,

> 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