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practical management science
Questions and Answers of
Practical Management Science
A bank is attempting to determine where its assets should be invested during the current year. At present,$500,000 is available for investment in bonds, home loans, auto loans, and personal loans.
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 70% chemical 1, and drug 2 must be at least 60% chemical 2. Up to 50,000 ounces of drug 1 can be sold at
A coal company produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons)
A chemical company produces three products, A, B, and C, and can sell these products in unlimited quantities at the following unit prices: A, $10; B, $55; and C, $100. Producing a unit of A requires
Abotte Products produces three products, A, B, and C. The company can sell up to 300 pounds of each product at the following prices (per pound): product A, $10; product B, $12; and product C, $20.
An investor has $100,000 to invest right now (the beginning of year 1). The cash flows associated with five available investments are listed in the file P04_61.xlsx. For example, every dollar
An oil company processes oil into aviation fuel and heating oil. It costs $65,000 to purchase each 1000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and 500 barrels
All steel manufactured by Allied Steel must meet the following requirements: between 3.2% and 3.5% carbon; between 1.8% and 2.5% silicon; between 0.9% and 1.2% nickel; tensile strength of at least
United Steel manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the
United Steel manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the
Federated Oil has refineries in Los Angeles and Chicago. The Los Angeles refinery can refine up to two million barrels of oil per year, and the Chicago refinery up to three million. After the oil is
A feed company produces two types of cattle feed, both consisting totally of wheat and alfalfa. Feed 1 must contain at least 80% wheat, and feed 2 must contain at least 60% alfalfa. Feed 1 sells for
Based on Thomas (1971). A toy company produces toys at two plants and sells them in three regions. The current demands at these regions are given in the file P04_72.xlsx. Each plant can produce up to
A bank needs exactly two employees working each hour from 9 a.m. to 5 p.m. Workers can work the shifts and are paid the wages listed in the file P04_74.xlsx. For example, a worker working 9 a.m. to 2
A rock company uses five types of rocks to fill four orders. The phosphate content, availability of each type of rock, and the production cost per pound for each rock are listed in the file
An automobile manufacturer needs to plan its production for the next year. Demands for the next 12 months are forecasted to be 940, 790, 360, 720, 270, 130, 160, 300, 990, 290, 280, and 790. Other
You want to take out a $300,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 6%. Twenty years from now, you will need to make a $40,000 ending balloon
Suppose you are planning for retirement. At the beginning of this year and each of the next 39 years, you plan to contribute some money to your retirement fund. Each year, you plan to increase your
Based on Brams and Taylor (2000). Suppose that Eli Lilly and Pfizer are going to merge. Merger negotiations must settle the following issues:■ What will the name of the merged corporation be?■
AdminaStar processes Medicare claims. At the beginning of month 1 they have a backlog of 40,000 difficult claims and 60,000 easy claims. The predicted claim volume for months 1 through 8 is listed in
Based on Charnes and Cooper (1955). A small company is trying to determine employee salary based on the following attributes: effectiveness, responsibility, initiative, experience, education,
You can calculate the risk index of an investment by taking the absolute values of percentage changes in the value of the investment for each year and averaging them. Suppose you are trying to
Based on Magoulas and Marinos-Kouris (1988). An oil company produces two products: regular and premium gasoline. Each product contains 0.15 gram of lead per liter. The two products are produced
Capsule Drugs manufactures two drugs. The drugs are produced by blending two chemicals. By weight, drug 1 must contain at least 65% chemical 1, and drug 2 must contain at least 55% chemical 1. Drug 1
Molecular Products produces three chemicals: B, C, and D. The company begins by purchasing chemical A for a cost of $650 per 100 liters. For an additional cost of $320 and the use of three hours of
Bexter Labs produces three products: A, B, and C. Bexter can sell up to 3000 units of product A, up to 2000 units of product B, and up to 2000 units of product C. Each unit of product C uses two
An automobile manufacturing company has a $1,500,000 advertising budget. To increase its auto-mobile sales, the company is considering advertising in newspapers and on television. The more the
Broker Sonya Wong is currently trying to maximize her profit in the bond market. Four bonds are available for purchase and sale at the bid and ask prices shown in the file P04_97.xlsx. Sonya can buy
Budget Auto produces inexpensive cars. Each car is sold for $7900. The raw material in a car costs $5000. Labor time and robot time are needed to produce cars. A worker can do the needed labor on, at
The ZapCon Company is considering investing in three projects. If it fully invests in a project, the realized cash flows (in millions of dollars) will be as listed in the file P04_99.xlsx. For
Aluminaca produces 100-foot-long, 200-foot-long, and 300-foot-long ingots for customers. This week’s demand for ingots is listed in the file P04_101.xlsx. Aluminaca has four furnaces in which
Each day, Eastinghouse produces capacitors during three shifts: 8 a.m.to 4 p.m., 4 p.m.to 12 a.m., and 12 a.m.to 8 a.m. The hourly salary paid to the employees on each shift, the price charged for
During the next three months, a heating and cooling company must meet (on time) the following demands for air conditioners: month 1, 300; month 2, 400; and month 3, 500. Air conditioners can be
Gotham City National Bank is open Monday through Friday from 9 a.m. to 5 p.m. From past experience, the bank knows that it needs the numbers of tellers listed in the file P04_104.xlsx. Gotham City
Based on Charnes and Cooper (1955). Alex Cornby makes his living buying and selling corn. On January 1, he has 5000 bushels of corn and $10,000 in cash. On the first day of each month, Alex can buy
City 1 produces 500 tons of waste per day, and city 2 produces 400 tons of waste per day. Waste must be incinerated at incinerator 1 or 2, and each incinerator can process up to 500 tons of waste per
Based on Smith (1965). Silicon Valley Corporation (Silvco) manufactures transistors. An important aspect of the manufacture of transistors is the melting of the element germanium (a major component
The Fresh Turkey Company produces two types of turkey cutlets for sale to fast-food restaurants. Each type of cutlet consists of white meat and dark meat. Cutlet 1 sells for $2.79 per pound and must
The production line employees at Grummins Engine work four days per week, 10 hours per day. Each day of the week, the following minimum numbers of line employees are needed: Monday through Friday, 70
Based on Lanzenauer et al. (1987). To process income tax forms, the IRS first sends each form through the data preparation (DP) department, where information is coded for computer entry. Then the
Based on Robichek et al. (1965). The Korvair Department Store has $100,000 in available cash. At the beginning of each of the next six months, Korvair will receive revenues and pay bills as listed in
Mackk Engine produces diesel trucks. New government emission standards have dictated that the aver-age pollution emissions of all trucks produced in the next three years cannot exceed 10 grams per
Sunco Oil has three different processes that can be used to manufacture various types of gasoline. Each process involves blending oils in the company’s catalytic cracker. Running process 1 for an
Flexco produces six products in the following manner. Each unit of raw material purchased yields 4 units of product 1, 2 units of product 2, and 1 unit of product 3. Up to 1200 units of product 1 can
Each week, Chemco can purchase unlimited quantities of raw material at $6 per pound. Each pound of purchased raw material can be used to produce either input 1 or input 2. Each pound of raw material
Bexter Labs produces three products: A, B, and C. Bexter can sell up to 2000 units of product A, up to 2500 units of product B, and up to 800 units of product C. Each unit of product C uses two units
Based on Franklin and Koenigsberg (1973). The city of Busville contains three school districts. The numbers of minority and nonminority students in each district are given in the file P04_121.xlsx.
Based on Carino and Lenoir (1988). Brady Corporation produces cabinets. Each week, Brady requires 90,000 cubic feet of processed lumber. The company can obtain lumber in two ways. First, it can
Based on Dobson and Kalish (1988). Chandler Enterprises produces two competing products, A and B. The company wants to sell these products to two groups of customers. The values each customer places
Based on Robichek et al. (1965). At the beginning of month 1, Finco has $4500 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills. (File
During each six-hour period of the day, the Bloomington Police Department needs at least the number of police officers shown in the file P04_125.xlsx. Po-lice officers can be hired to work either 12
Based on Glassey and Gupta (1978). A paper recycling plant processes box board, tissue paper, news-print, and book paper into pulp that can be used to produce three grades of recycled paper. The
Three bonds, as listed in the file P04_127.xlsx, are currently for sale. Each bond has a face value of $100. Every six months, starting six months from the current date and ending at the expiration
You have been assigned to develop a model that can be used to schedule employees at a local fast-food restaurant. Assume that computer technology has advanced to the point where very large problems
You have been assigned to develop a model that can be used to schedule the nurses working in a maternity ward.a. What data would you collect as inputs to your model?b. Describe in words several
In this chapter, we give you the cost of producing a product and other inputs that are used in the analysis. Do you think most companies find it easy to deter-mine the cost of producing a product?
Keefer Paper produces recycled paper from paper purchased from local offices and universities. The company sells three grades of paper: high-brightness paper, medium-brightness paper, and
For the distribution data shown in Table 5.10, what is the least-cost assignment of truckloads to carriers that meets the necessary requirements? What is the cost of this distribution plan?epilogue
In the Grand Prix example with varying tax rates, the optimal solution more than satisfies customer demands. Modify the model so that regions have not only lower limits on the amounts they require,
In the Grand Prix example with varying tax rates, the optimal solution uses all available plant capacity and more than satisfies customer demands. Will this always be the case? Experiment with the
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
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
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
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
In Example 7.5, 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
Starting with the solution to the advertising selection problem in Example 7.6, suppose the company, for whatever reason, cannot place ads on “Sports Center.” Make the appropriate changes in the
In judging the fit of the estimated response function in Example 7.5, you could use MAE (mean absolute error) instead of RMSE. MAE is the average of the absolute prediction errors.a. When you
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,
In the electricity pricing model in Example 7.4, we assumed that the capacity level is a decision variable. Assume now that capacity has already been set at 0.700 million of mWh. Change the model
In the complementary-product pricing model in Example 7.3, the SolverTable results in Figure 7.21 indicate that the company can sometimes increase overall profit by selling suits below cost. How far
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