Questions and Answers of Optimization

Tucker Inc. produces high-quality suits and sport coats for men. Each suit requires 1.2 hours of cutting time and 0.7 hours of sewing time, uses 6 yards of material, and provides a profit
The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual racetracks. Because safety is a primary consideration at such events, many
Davison Electronics manufactures two LCD television monitors, identified as model A and model B. Each model has its lowest possible production cost when produced on Davisonâ€™s new production
Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as
Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7%
Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 hours will be required to complete the project. The
Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine
National Insurance Associates carries an investment portfolio of stocks, bonds, and other investment alternatives. Currently $200,000 of funds are available and must be considered for new investment
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to
Benson Electronics manufactures three components used to produce cell telephones and other communication devices. In a given production period, demand for the three components may exceed
Golf Shafts, Inc. (GSI) produces graphite shafts for several manufacturers of golf clubs. Two GSI manufacturing facilities, one located in San Diego and the other in Tampa, have the capability to
The Pfeiffer Company manages approximately $15 million for clients. For each client, Pfeiffer chooses a mix of three investment vehicles: a growth stock fund, an income fund, and a money market fund.
La Jolla Beverage Products is considering producing a wine cooler that would be a blend of a white wine, a rosé wine, and fruit juice. To meet taste specifications, the wine cooler must consist of
The program manager for Channel 10 would like to determine the best way to allocate the time for the 11:00–11:30 evening news broadcast. Specifically, she would like to determine the number of
Gulf Coast Electronics is ready to award contracts for printing their annual report. For the past several years, the four-color annual report has been printed by Johnson Printing and Lakeside Litho.
PhotoTech, Inc., a manufacturer of rechargeable batteries for digital cameras, signed a contract with a digital photography company to produce three different lithium-ion battery packs for a new line
TJâ€™s, Inc., makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing
J. D. Williams, Inc., is an investment advisory firm that manages more than $120 million in funds for its numerous clients. The company uses an asset allocation model that recommends the portion of
Reep Construction recently won a contract for the excavation and site preparation of a new rest area on the Pennsylvania Turnpike. In preparing his bid for the job, Bob Reep, founder and president of
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this yearâ€™s program. Advertising alternatives
The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor
The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests
Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows:Consumer tests with coffee products were
Ajax Fuels, Inc., is developing a new additive for airplane fuels. The additive is a mixture of three ingredients: A, B, and C. For proper performance, the total amount of additive (amount of A+
G. Kunz and Sons, Inc., manufactures two products used in the heavy equipment industry. Both products require manufacturing operations in two departments. The following are the production time (in
As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars):The annual payments must be
The Clark County Sheriff’s Department schedules police officers for 8-hour shifts. The beginning times for the shifts are 8:00 A.M., noon, 4:00 P.M., 8:00 P.M., midnight, and 4:00 A.M. An officer
Reconsider the Welte Mutual Funds problem from Section 9.2. Define your decision variables as the fraction of funds invested in each security. Also, modify the constraints limiting investments in
An investment advisor at Shore Financial Services wants to develop a model that can be used to allocate investment funds among four alternatives: stocks, bonds, mutual funds, and cash. For the coming
Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the companyâ€™s needs. In
The Atlantic Seafood Company (ASC) is a buyer and distributor of seafood products that are sold to restaurants and specialty seafood outlets throughout the Northeast. ASC has a frozen storage
Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the storeâ€™s leading products use the Romans Food Market name: Romans
The production manager for the Classic Boat Corporation must determine how many units of the Classic 21 model to produce over the next four quarters. The company has a beginning inventory of 100
Seastrand Oil Company produces two grades of gasoline: regular and high octane. Both gasolines are produced by blending two types of crude oil. Although both types of crude oil contain the two
The Ferguson Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 11/2, 21/2, and 31/2
Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a
The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by truck. The company recently contracted to supply gasoline distributors in southern Ohio, and it has $600,000
The Silver Star Bicycle Company will be manufacturing both menâ€™s and womenâ€™s models for its Easy-Pedal 10-speed bicycles during the next two months. Management wants to develop a
Filtron Corporation produces filtration containers used in water treatment systems. Although business has been growing, the demand each month varies considerably. As a result, the company utilizes a
Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3300 bookshelf speakers and 4100 floor speakers over the
TriCity Manufacturing (TCM) makes Styrofoam cups, plates, and sandwich and meal containers. Next weekâ€™s schedule calls for the production of 80,000 small sandwich containers, 80,000 large
EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 9000 windows in inventory.
Morton Financial must decide on the percentage of available funds to commit to each of two investments, referred to as A and B, over the next four periods. The following table shows the amount of new
Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the
The Flamingo Grill is an upscale restaurant located in St. Petersburg, Florida. To help plan an advertising campaign for the coming season, Flamingoâ€™s management team hired the advertising
Phoenix Computer manufactures and sells personal computers directly to customers. Orders are accepted by phone and through the company’s Web site. Phoenix will be introducing several new laptop
The Scottsville Textile Mill1 produces five different fabrics. Each fabric can be woven on one or more of the millâ€™s 38 looms. The sales departmentâ€™s forecast of demand for the next
Davis Instruments has two manufacturing plants located in Atlanta, Georgia. Product demand varies considerably from month to month, causing Davis extreme difficulty in workforce scheduling. Recently
Duke Energy manufactures and distributes electricity to customers in the United States and Latin America. Duke recently purchased Cinergy Corporation, which has generating facilities and energy
Reconsider the Leisure Airlines problem from Section 12.1. The demand forecasts shown in Table represent Leisure Air€™s best estimates of demand. But because demand cannot be forecasted
Reconsider the Leisure Airlines problem from Section 12.1. Suppose that as of May 1 the following number of seats have been sold:a. Determine how many seats are still available for sale on each
Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes
In the latter part of Section 12.2 we developed a moderate risk portfolio model for Hauck Investment Services. Modify the model given so that it can be used to construct a portfolio for more
Table shows data on the returns over five 1-year periods for six mutual funds. A firm€™s portfolio managers will assume that one of these scenarios will accurately reflect the investing
Consider the problemMin2X2 - 20X + 2XY + Y2 - 14Y + 58s.t. X + 4Y ≤ 8a. Find the minimum solution to this problem.b. If the right-hand side of the constraint is increased from 8 to 9, how much do
GreenLawns provides a lawn fertilizer and weed control service. The company is adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers.
The functionf(X, Y) = 3(1 - X)2e(- X2-(Y+1)2) €“ 10(x/5 €“ X3 €“ Y5)e(-X2 €“ Y2) €“ e(-(X+1) €“ Y2)/3was used to generate Figures (a) and
The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the formf (L, C) = c0Lc1Cc2Where c0, c1, and c2 are constants.
Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function:S = 20L0.30C0.70In
The profit function for two products isProfit = -3x12 + 42x1 – 3x22 + 48x2 + 700Where x1 represents units of production of product 1 and x2 represents units of production of product 2. Producing
Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of
Harry Markowitz received the 1990 Nobel Prize for his path-breaking work in portfolio optimization. One version of the Markowitz model is based on minimizing the variance of the portfolio subject to
Many forecasting models use parameters that are estimated using nonlinear optimization. This is true of many of the models developed in Chapter 6. Consider the exponential smoothing forecasting model
The purpose of this exercise is to learn how to calculate stock returns for portfolio models using actual stock price data. First, it is necessary to obtain stock price data. One source (of many) is
Formulate and solve the Markowitz portfolio optimization model that was introduced in Problem 14 using the data from Problem 16. In this case, nine scenarios correspond to the yearly returns from
Using the data obtained in Problem 16, construct a portfolio from Apple, AMD, and Oracle that matches the Information Technology S&P index as closely as possible. Use the return data for the
Most investors are happy when their returns are â€œabove average,â€ but not so happy when they are â€œbelow average.â€ In the Markowitz portfolio optimization model in Problem 14,
This problem requires a basic understanding of the normal probability distribution. Investors are often interested in knowing the probabilities of poor returns. For example, for what cutoff return
Options are popular instruments in the world of finance. A call option on a stock gives the owner the right to buy the stock at a predetermined price before the expiration date of the option. For
The port of Lajitas has three loading docks. The distance (in meters) between the loading docks is given in the table below:Three tankers currently at sea are coming into Lajitas. It is necessary to
Andalus Furniture Company has two manufacturing plants, one at Aynor and another at Spartanburg. The cost in dollars of producing a kitchen chair at each of the two plants is given here.Aynor: Cost =
This case is based on the Q.M. in Action, Pricing for Environmental Compliance in the Auto Industry. In this case we build a model similar to the one built for General Motors. The CAFE requirement on
Indicate which of the following is an all-integer linear program and which is a mixed-integer linear program. Write the LP Relaxation for the problem but do not attempt to solve.a. Max 30x1 +
Consider the following all-integer linear program:Max 5x1 + 8x2s.t.6x1 + 5x2 ≤ 309x1 + 4x2 ≤ 36 1 x1 + 2 x2 ≤ 10 x1, x2 ≥ 0 and integera. Graph the constraints for this
Consider the following all-integer linear program:Max 1x1 + 1x2s.t.4x1 + 6x2 ≤ 221x1 + 5x2 ≤ 152x1 + 1x2 ≤ 9 x1, x2 ≥ 0 and integera. Graph the constraints for this problem.
Consider the following all-integer linear program:Max 10x1 + 3x2s.t.6x1 + 7x2 ≤ 403x1 + 1x2 ≤ 11 x1, x2 ≥ 0 and integera. Formulate and solve the LP Relaxation of the problem. Solve
Consider the following mixed-integer linear program:Max 2x1 + 3x2s.t.4x1 + 9x2 ≤ 367x1 + 5x2 ≤ 35 x1, x2 ≥ 0 and x1 integera. Graph the constraints for this problem. Indicate on
Consider the following mixed-integer linear program:Max 1x1 + 1x2s.t.7x1 + 9x2 ≤ 639x1 + 5x2 ≤ 453x1 + 1x2 ≤ 12 x1, x2 ≥ 0 and x2 integera. Graph the constraints for this problem.
The following questions refer to a capital budgeting problem with six projects represented by 0-1 variables x1, x2, x3, x4, x5, and x6:a. Write a constraint modeling a situation in which two of the
Spencer Enterprises is attempting to choose among a series of new investment alternatives. The potential investment alternatives, the net present value of the future stream of returns, the capital
Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the
Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered
Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:During the next
Yates Company supplies road salt to county highway departments. The company has three trucks, and the dispatcher is trying to schedule tomorrow€™s deliveries to Polk, Dallas, and Jasper
Recall the Martin-Beck Company distribution system problem in Section 11.3.a. Modify the formulation shown in Section 11.3 to account for the policy restriction that one plant, but not two, must be
An automobile manufacturer has five outdated plants: one each in Michigan, Ohio, and California and two in New York. Management is considering modernizing these plants to manufacture engine blocks
CHB, Inc., is a bank holding company that is evaluating the potential for expanding into a 13-county region in the southwestern part of the state. State law permits establishing branches in any
The Northshore Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank including adequate customer
Refer to the Ohio Trust bank location problem introduced in Table shows the counties under consideration and the adjacent counties.TABLECOUNTIES IN THE OHIO TRUST EXPANSION REGIONCounties Under
Refer to the Salem Foods share of choices and address the following issues. It is rumored that Kingâ€™s is getting out of the frozen pizza business. If so, the major competitor for Salem Foods
Burnside Marketing Research conducted a study for Barker Foods on some designs for a new dry cereal. Three attributes were found to be most influential in determining which cereal had the best taste:
Refer to Problem 14. Suppose that management determined that its cost estimates to modernize the New York plants were too low. Specifically, suppose that the actual cost is $40 million to modernize
The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of the eight display rooms that Bayside uses for exhibitions is shown in
The Delta Group is a management consulting firm specializing in the health care industry. A team is being formed to study possible new markets, and a linear programming model has been developed for
Roedel Electronics produces a variety of electrical components, including a remote controller for televisions and a remote controller for DVD players. Each controller consists of three subassemblies
A mathematical programming system named SilverScreener uses a 0-1 integer programming model to help theater managers decide which movies to show on a weekly basis in a multiple-screen theater
East Coast Trucking provides service from Boston to Miami using regional offices located in Boston, New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, Florence, Savannah, Jacksonville,
ASW Publishing, Inc., a small publisher of college textbooks, must make a decision regarding which books to publish next year. The books under consideration are listed in the following table, along
Using aggressive mail promotion with low introductory interest rates, Yeager National Bank (YNB) built a large base of credit card customers throughout the continental United States. Currently, all

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