Question: Union Express has 60 tons of cargo

> An automobile manufacturer is considering mechanical design changes in one of its top-selling cars to reduce the weight of the car by at least 400 pounds to improve its fuel efficiency. Design engineers have identified 10 changes that could be made in th

> The Mega-Bucks Corporation is planning its production schedule for the next four weeks and is forecasting the following demand for compound X—a key raw material used in its production process: The company currently has no compound X o

> Bavarian Motor Company (BMC) manufacturers cars and SUVs in Europe and ships them to distributors in the United States. Presently, BMC has an inventory of 200 cars and 140 SUVs in Newark, NJ and 300 cars and 180 SUVs in Jacksonville, FL. These vehicles n

> Dan Boyd is a financial planner trying to determine how to invest $100,000 for one of his clients. The cash flows for the five investments under consideration are summarized in the following table: For example, if Dan invests $1 in investment A at the b

> MasterDebt is a national credit card company with thousands of card holders located across the United States. Every day throughout the month, MasterDebt sends out statements to different customers summarizing their charges for the previous month. Custome

> The Clamped Oil Company has a tanker truck that it uses to deliver fuel to customers. The tanker has five different storage compartments with capacities to hold 2,500, 2,000, 1,500, 1,800 and 2,300 gallons, respectively. The company has an order to deliv

> Consider the following optimization problem: a. What is the optimal solution to this LP problem? b. Now suppose that X1 and X2 must be integers. What is the optimal solution? c. What general principle of integer programming is illustrated by this questi

> Clamped Oil purchases crude oil products from suppliers in Texas (TX), Oklahoma (OK), Pennsylvania (PA), and Alabama (AL), from which it refines four end-products: gasoline, kerosene, heating oil, and asphalt. Because of differences in the quality and ch

> A company manufactures three products: A, B, and C. The company currently has an order for 3 units of product A, 7 units of product B, and 4 units of product C. There is no inventory for any of these products. All three products require special processin

> GLMH Shipping is a start-up company that plans to offer same-day shipping services between 20 major cities in the United States. In order to provide this service, GLMH needs to build hubs at airports in several of these cities. GLMH wants to select hub l

> Suppose plants 1 and 2 represent different building alternatives for the same site (i.e., only one of these plants can be built). Similarly, suppose plants 4 and 5 represent different building alternatives for another site. a. What additional constraints

> A manufacturer is considering alternatives for building new plants in order to be located closer to three of its primary customers with whom it intends to develop long-term relationships. The net cost of manufacturing and transporting each unit of the pr

> Howe’s Carpet World has just received an order for carpets for a new office building. The order is for 4,000 yards of carpet 4-feet wide, 20,000 yards of carpet 9-feet wide, and 9,000 yards of carpet 12-feet wide. Howie can order two kinds of carpet rol

> Bellows Lumber Yard, Inc. stocks standard length, 25-foot boards, which it cuts to custom lengths to fill individual customer orders. An order has just come in for 5,000 7-foot boards, 1,200 9-foot boards, and 300 11-foot boards. The lumber yard manager

> A real estate developer is planning to build an apartment building specifically for graduate students on a parcel of land adjacent to a major university. Four types of apartments can be included in the building: efficiencies, and one-, two-, or three-bed

> The demand for electricity varies greatly during the day. Because large amounts of electricity cannot be stored economically, electric power companies cannot manufacture electricity and hold it in inventory until it is needed. Instead, power companies mu

> Tropic sun is a leading grower and distributor of fresh citrus products with three large citrus groves scattered around central Florida in the cities of Mt. Dora, Eustis, and Clermont. Tropic sun currently has 275,000 bushels of citrus at the grove in Mt

> A developer of video game software has seven proposals for new games. Unfortunately, the company cannot develop all the proposals because its budget for new projects is limited to $950,000 and it has only 20 programmers to assign to new projects. The fin

> Identify reasonable values for M12 and M22 in the example on quantity discounts presented in section 6-16b of this chapter.

> The teenage daughter of a recently deceased movie star inherited a number of items from her famous father’s estate. Rather than convert these assets to cash immediately, her financial advisor has recommended that she let some of these a

> Radford Castings can produce brake shoes on six different machines. The following table Summary zes the manufacturing costs associated with producing the brake shoes on each Machine along with the available capacity on each machine. If the company has r

> Charles Mc Keown is an acquisitions editor for a college textbook publisher. The file Books.xlsx that accompanies this book contains a list of 151 textbooks that Charles has an opportunity to acquire from another publisher. For each title, the file lists

> Health Care Systems of Florida (HCSF) is planning to build a number of new emergencycare clinics in central Florida. HCSF management has divided a map of the area into seven regions. They want to locate the emergency centers so that all seven regions wil

> A power company is considering how to increase its generating capacity to meet expected demand in its growing service area. Currently, the company has 750 megawatts (MW) of generating capacity but projects it will need the following minimum generating ca

> A manufacturer of industrial motors has identified ten new prospective customers for its products with estimated each customer’s annual sales potential as follows: The company would like to allocate these ten prospective customers to f

> Snookers Restaurant is open from 8:00 am to 10:00 pm daily. Besides the hours they are open for business, workers are needed an hour before opening and an hour after closing for setup and clean-up activities. The restaurant operates with both full-time a

> Bowden Transport provides dispatching services for independent truckers who specialize in transporting cars purchased online from the seller to the buyer. At present, there are four cars needing to be picked up and delivered and five trucks in the vicini

> Joni Wu manages the Gold Rush Casino in New Orleans. She would like to adjust the assortment of gaming machines in the casino to ensure they are operating in the most profitable manner. The following table summarizes the current assortment of gaming mach

> Garden City Beach is a popular summer vacation destination for thousands of people. Each summer, the city hires temporary lifeguards to ensure the safety of the vacationing public. Garden City’s lifeguards are assigned to work five cons

> Ken Stark is an operations analyst for an insurance company in Muncie, Indiana. Over the next 6 weeks the company needs to send 2,028,415 pieces of marketing literature to customers in the following 16 states: In order to coordinate with other marketing

> As shown in Figure 6.1, the feasible region for an ILP consists of a relatively small, finite number of points, whereas the feasible region of its LP relaxation consists of an infinite number of points. Why, then, are ILPs so much harder to solve than LP

> As rush coordinator for the Alpha Beta Chi (ABC) sorority, Kim Wong asked each pledge to identify five existing members of ABC whom she would most like to have as a big sister. Kim then asks the pledges to rank order these potential big sisters from 5 do

> Suppose the x’s in the following table indicate locations where fire sprinkler heads need to be installed in an existing building. The s indicates the location of the water source to supply these sprinklers. Assume pipe can only be run

> Draw the network representation of the following network flow problem. What kind of network flow problem is this? MIN: 12X13 16X14 15X15 14X23 13X24 17X25 Subject to: 2 X13 2 X14 2 X15 5 28 2 X23 2 X24 2 X25 5 27 1 X13 1 X23 5 15 1 X14 1 X24 5 15 1

> Draw the network representation of the following network flow problem. MIN: 1 7X12 1 6X14 1 3X23 1 4X24 1 5X32 1 9X43 1 8X52 1 5X54 Subject to: 2X12 2 X14 5 2 5 1 X12 1 X52 1 X32 2 X23 2 X24 5 1 4 2 X32 1 X23 1 X43 5 1 8 1 X14 1 X24 1 X54 2 X43 5 1

> Consider the generalized transportation problem shown in Figure 5.35. How can this problem be transformed into an equivalent transportation problem? Draw the network for the equivalent problem.

> Consider the revised Coal Bank Hollow recycling problem discussed in Section 5-5d of this chapter. We said that it is safest to assume the supply in a generalized network flow problem is capable of meeting the demand (until Solver proves otherwise). a. S

> Refer to question 6. Suppose that service at the drive-in window is provided at a rate of 40 customers per hour and follows an exponential distribution. a. What is the expected service time per customer? b. Use equation 13.2 to determine the probability

> The manager of catering services for the Roan oker Hotel has a problem. The banquet hall at the hotel is booked each evening during the coming week for groups who have reserved the following numbers of tables: The hotel has 500 tablecloths that can be u

> A building contractor is designing the ductwork for the heating and air conditioning system in a new, single-story medical building. Figure 5.45 summarizes the possible connections between the primary air handling unit (node 1) and the various air outlet

> The U.S. Department of Transportation (DOT) is planning to build a new interstate to run from Detroit, Michigan, to Charleston, South Carolina. A number of different routes have been proposed and are summarized in Figure 5.44, where node 1 represents Det

> A new airport being built will have three terminals and two baggage pickup areas. An automated baggage delivery system has been designed to transport the baggage from each terminal to the two baggage pickup areas. This system is depicted graphically in F

> The Britt’s & Estragon company manufactures small engines at three different plants. From the plants, the engines are transported to two different warehouse facilities before being distributed to three wholesale distributors. The pe

> Refer to the equipment replacement problem discussed in Section 5-3 of this chapter. In addition to the lease costs described for the problem, suppose that it costs Compu-Train $2,000 extra in labor costs whenever the company replaces their existing comp

> E-mail messages sent over the Internet are broken up into electronic packets that may take a variety of different paths to reach their destination where the original message is reassembled. Suppose the nodes in the graph shown in Figure 5.42 represent a

> Alaskan Railroad is an independent, stand-alone railroad operation not connected to any other rail service in North America. As a result, rail shipments between Alaska and the rest of North America must be shipped by truck for thousands of miles or loade

> Telephone calls for the Yak Line, a discount long distance carrier, are routed through a variety of switching devices that interconnect various network hubs in different cities. The maximum number of calls that can be handled by each segment of their net

> Joe Jones wants to establish a construction fund (or sinking fund) to pay for a new bowling alley he is having built. Construction of the bowling alley is expected to take 6 months and cost $300,000. Joe’s contract with the construction

> The state of Virginia is one of the largest producers of wood furniture in the United States, with the furniture industry accounting for 50% of value added to wood materials. Over the past 40 years the inventory volume of wood in Virginiaâ€&#1

> A residential moving company needs to move a family from city 1 to city 12 in Figure 5.40 where the numbers on the arcs represent the driving distance in miles between cities. a. Create a spreadsheet model for this problem. b. What is the optimal solut

> Omega Airlines has several nonstop flights between Atlanta and Los Angeles every day. The schedules of these flights are shown in the following table. Omega wants to determine the optimal way of assigning flight crews to these different flights. The com

> The Conch Oil Company needs to transport 30 million barrels of crude oil from a port in Doha, Qatar in the Persian Gulf to three refineries throughout Europe. The refineries are in Rotterdam, Netherlands; Toulon, France; and Palermo, Italy, and they req

> An information systems consultant who lives in Dallas must spend the majority of the month of March onsite with a client in San Diego. Her travel schedule for the month is as follows: The usual round-trip ticket price between Dallas and San Diego is $75

> To use the balance-of-flow rule presented in this chapter, constraints for supply nodes must have negative RHS values. Some LP software packages cannot solve problems in which the constraints have negative RHS values. How could these constraints be modif

> The graph in Figure 5.38 represents various flows that can occur through a sewage treatment plant with the numbers on the arcs representing the maximum flow (in tons of sewage per hour) that can be accommodated. Formulate an LP model to determine the max

> A furniture manufacturer has warehouses in cities represented by nodes 1, 2, and 3 in Figure 5.37. The values on the arcs indicate the per unit shipping costs required to transport living room suites between the various cities. The supply of living room

> The blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. The supply and demand for donated blood is shown in Figure

> A cotton grower in south Georgia produces cotton on farms in Statesboro and Brooklet, ships it to cotton gins in Claxton and Millen where it is processed, and then sends it to distribution centers in Savannah, Perry, and Valdosta where it is sold to cust

> If your home or office is carpeted, there’s a good chance that carpet came from Dalton, Georgia— also known as the “Carpet Capital of the World.” Manufacturers in the Dalton area pro

> The Ortega Food Company needs to ship 100 cases of hot tamales from its warehouse in San Diego to a distributor in New York City at minimum cost. The costs associated with shipping 100 cases between various cities are listed in the following table: a.

> Jacobs Manufacturing produces a popular custom accessory for pick-up trucks at plants in Huntington, West Virginia and Bakersfield, California, and ships them to distributors in Dallas, Texas; Chicago, Illinois; Denver, Colorado; and Atlanta, Georgia. Th

> Sunrise Swimwear manufactures ladies swimwear in January through June of each year that is sold through retail outlets in March through August. The following table summarizes the monthly production capacity and retail demand (in 1000s), and production an

> A construction company wants to determine the optimal replacement policy for the earth mover it owns. The company has a policy of not keeping an earth mover for more than 5 years, and has estimated the annual operating costs and trade-in values for earth

> Trejo Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next 4 months is shown in the following table along with the expected production costs and the exp

> This chapter followed the convention of using negative numbers to represent the supply at a node and positive numbers to represent the demand at a node. Another convention is just the opposite—using positive numbers to represent supply and negative numbe

> Use Solver to create Answer and Sensitivity Reports for question 25 at the end of Chapter 2 and answer the following questions: a. How much can the price of watermelons drop before it is no longer optimal to plant any watermelons? b. How much does the pr

> Use Holt-Winter’s multiplicative method to create a seasonal model that minimizes the MSE for the data set. Use Solver to determine the optimal values of a, b, and g. a. What are the optimal values of a, b, and g? b. Prepare a line graph comparing the pr

> Use Solver to create Answer and Sensitivity Reports for question 23 at the end of Chapter 2 and answer the following questions: a. If the profit on Razors decreased to $35, would the optimal solution change? b. If the profit on Zoom ers decreased to $35,

> Use Holt-Winter’s additive method to create a seasonal model that minimizes the MSE for the data set. Use Solver to determine the optimal values of a, b, and g. a. What are the optimal values of a, b, and g? b. Prepare a line graph comparing the predict

> The United States is the biggest consumer of natural gas, and the second largest natural gas producer in the world. According to the U.S. Energy Information Administration (EIA), the United States consumed 26.7 trillion cubic feet of natural gas in 2014.

> Adrian is the new Vice President for operations at The Golfer’s Link (TGL), a company specializing in the production of quality, discount sets of golf clubs. Adrian was hired primarily because of his expertise in supply chain management

> Find two numbers whose difference is 19 and whose product is a minimum.

> Find two numbers whose sum is 19 and whose product is a maximum.

> express the given quantity as a function (x) of one variable x. The perimeter of a rectangle of length x and width y that has an area of 200 square meters

> express the given quantity as a function (x) of one variable x. The volume of a right circular cylinder of diameter x and height equal to twice the diameter

> express the given quantity as a function (x) of one variable x. The volume of a sphere of diameter x.

> express the given quantity as a function f1x2 of one variable x. The sum of two numbers x and y whose product is 36.

> Find the conditional probability, in a single roll of two fair dice, that. The roll is doubles, given that the sum is 10.

> A large grocery chain found that, on average, a checker can recall P% of a given price list x hours after starting work, as given approximately by At what time x does the checker recall a maximum percentage? What is the maximum?

> Two heavily industrial areas are located 10 miles apart, as shown in the figure. If the concentration of particulate matter (in parts per million) decreases as the reciprocal of the square of the distance from the source, and if area A1 emits eight times

> Some birds tend to avoid flights over large bodies of water during daylight hours. Suppose that an adult bird with this tendency is taken from its nesting area on the edge of a large lake to an island 5 miles offshore and is then released (see the figure

> The concentration C(t), in milligrams per cubic centimeter, of a particular drug in a patient’s blood stream is given by where t is the number of hours after the drug is taken. How many hours after the drug is taken will the concentra

> The cost per hour for fuel to drive a rental truck from Chicago to New York, a distance of 800 miles, is given by where v is the speed of the truck in miles per hour. Other costs are $40 per hour. How fast should you drive to minimize the total cost

> A tool company has a uniform annual demand for 9,000 premium chainsaws. It costs $5 to store a chainsaw for a year and $2,500 to set up the plant for manufacture of the premium model. How many chainsaws should be manufactured in each production run in or

> A pharmacy has a uniform annual demand for 200 bottles of a certain antibiotic. It costs $10 to store one bottle for one year and $40 to place an order. How many times during the year should the pharmacy order the antibiotic in order to minimize the tota

> If the owner wants to enclose a rectangular area of 12,100 square feet as in Problem 35, what are the dimensions of the area that requires the least fencing? How many feet of fencing are required?

> If a builder has only $840 to spend on a fence, but wants to use both $6 and $18 per foot fencing as in Problem 33, what is the maximum area that can be enclosed? What are its dimensions?

> A parcel delivery service will deliver a package only if the length plus girth (distance around) does not exceed 108 inches. (A) Find the dimensions of a rectangular box with square ends that satisfies the delivery service’s restrictio

> Find the conditional probability, in a single roll of two fair dice, that. The sum is 10, given that the roll is doubles.

> A commercial pear grower must decide on the optimum time to have fruit picked and sold. If the pears are picked now, they will bring 30¢ per pound, with each tree yielding an average of 60 pounds of salable pears. If the average yield per tree increases

> A 300-room hotel in Las Vegas is filled to capacity every night at $80 a room. For each $1 increase in rent, 3 fewer rooms are rented. If each rented room costs $10 to service per day, how much should the management charge for each room to maximize gross

> A university student center sells 1,600 cups of coffee per day at a price of $2.40. (A) A market survey shows that for every $0.05 reduction in price, 50 more cups of coffee will be sold. How much should the student center charge for a cup of coffee in

> The following table contains price– demand and total cost data for the production of regular sleeping bags, where p is the wholesale price (in dollars) of a sleeping bag for an annual demand of x sleeping bags and C is the total cost (i

> Repeat Problem 21 for Data from Problem 21: (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government de

> A company manufactures and sells x cameras per week. The weekly price–demand and cost equations are, respectively, p = 400 - 0.5x and C(x) = 2,000 + 200x (A) What price should the company charge for the cameras, and how many cameras should be produced

> Find the dimensions of a rectangle with a perimeter of 76 feet that has the maximum area.

> Find the dimensions of a rectangle with an area of 108 square feet that has the minimum perimeter.

> Find two positive numbers whose product is 19 and whose sum is a minimum.

> Refer to the graph of y =(x) shown here. Find the absolute minimum and the absolute maximum over the indicated interval.

> There are 10 senators (half Democrats, half Republicans) and 16 representatives (half Democrats, half Republicans) who wish to serve on a joint congressional committee on tax reform. An 8-person committee is chosen at random from those who wish to serve.