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Questions and Answers of Statistics

Ever since the introduction of the first home video systems for television, Steve Goodman has dreamed about manufacturing his own video system for professionals. During the early years of home video,
The Marriott Tub Company manufactures two lines of bathtubs, called model A and model B. Every tub requires a certain amount of steel and zinc; the company has available a total of 25,000 pounds of
The Sweet Smell Fertilizer Company markets bags of manure labeled "not less than 60 pounds dry weight." The packaged manure is a combination of compost and sewage wastes. To provide good-quality
The National Credit Union has $250,000 available to invest in a 12-month commitment. The money can be placed in Treasury notes yielding an 8% return or in municipal bonds at an average rate of return
The advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure possible for the product within the $100,000 advertising budget ceiling placed upon it. To do so,
In June 1980, Harry Sinclair, General Manager of the Texas Division of Agri-Chem Corporation, received notification from Ben Elliot of Enerco that natural gas supplies were being rapidly depleted. In
Bob Bell's fortieth birthday party promised to be the social event of the year in Cookeville. To prepare, Bob stocked up on the following liquors:LIQUOR AMOUNT ON HAND (OUNCES)Bourbon
Marc Smith's construction firm currently has three projects under way in various counties in Iowa. Each requires a specific supply of gravel. Three gravel pits are available in Iowa to provide for
Ginny Rait is the general manager for N.R.G., Inc., a company producing two types of electric generators - the BR54 and the BR49. Orders have been received, and a production schedule is to be set up
Stockbroker Suzan Shader has made the following recommendations to her client:The client agrees to this list but provides several conditions:(1) No more than $2000 can be invested,(2) The money is to
Golding Manufacturing has four new jobs that must be assigned to any of four available machines. The cost of doing each job on each machine is as follows:Formulate this as a 0-1 integer programming
Harris Segal, marketing director for North-Central Power and Light, is about to begin an advertising campaign promoting energy conservation. In trying to budget between television and newspaper
Solve Problem 10-37 using QM for Windows. How many people, in total, will read or hear the advertisements?
Milborne Manufacturing produces three types of electric blenders - the Standard, the Deluxe, and the Chef's Delight. Production of the Standard model takes 1.5 hours, the deluxe model takes 2 hours,
Refer to Problem 10-39. Suppose that the first goal is twice as important as goals 2, 3, and 4; and the first goal is three times as important as the profit goal. Formulate this as a goal-programming
How do the graphical and simplex methods of solving LP problems differ? In what ways are they the same? Under what circumstances would you prefer to use the graphical approach?
You have just formulated an LP problem with 12 decision variables and eight constraints. How many basic variables will there always be? What is the difference between a basic and a nonbasic variable?
What are the simplex rules for selecting the pivot column? The pivot row? The pivot number?
How do maximization and minimization problems differ when applying the simplex method?
A particular LP problem has the following objective function:Maximize profit = $8X1 + $6X2 + $12X3 – $2X4Which variable should enter at the second simplex tableau? If the objective function
Explain the relationship between each number in a primal and corresponding numbers in the dual.
The first constraint in the High Note example in this chapter is 2X1 + 4X2 ≤ 80 (hours of electrician time available) Table M7.17 gives the final simplex tableau for this example on page M7-34.
The Dreskin Development Company is building two apartment complexes. It must decide how many units to construct in each complex subject to labor and material constraints. The profit generated for
Consider the following LP problem:(a) Convert these constraints to equalities by adding the appropriate slack, surplus, or artificial variables. Also, add the new variables into the problems
Solve the following LP problem graphically. Then set up a simplex tableau and solve the problem using the simplex method. Indicate the corner points generated at each iteration by the simplex method
Consider the following LP problem:Maximize profit = 10X1 + 8X2Subject to 4X1 + 2X2 ≤ 80X1 + 2X2 ≤ 50X1, X2 ≥ 0(a) Solve this problem graphically.(b) Set up the initial simplex tableau. On the
Solve the following LP problem first graphically and then by the simplex algorithm:Maximize profit = 4X1 + 5X2Subject to X1 + 2X2 ≥ 80 3X1 + X2 ≥ 75 X1, X2 ≥ 0What are the
Solve the following problem by the simplex method. What condition exists that prevents you from reaching an optimal solution?Maximize profit = 6X1 + 3X2Subject to 2X1 – 2X2 ≤ 2–X1 + X2 ≤ 1X1,
Consider the following financial problem:Maximize profit = $2X1 + $3X2Subject to 6X1 + 9X2 ≤ 189X1 + 3X2 ≥ 9X1, X2 ≥ 0(a) Find the optimal solution using the simplex method.(b) What evidence
At the third iteration of a particular LP maximization problem, the tableau at the bottom of this page is established. What special condition exists as you improve the profit and move to the next
A pharmaceutical firm is about to begin production of three new drugs. An objective function designed to minimize ingredient costs and three production constraints are as follows:Maximize profit =
The Bitz-Karan Corporation faces a blending decision in developing a new cat food called Yum-Mix. Two basic ingredients have been combined and tested, and the firm has determined that to each can of
The Roniger Company produces two products: bed mattresses and box springs. A prior contract requires that the firm produce at least 30 mattresses or box springs, in any combination. In addition,
Each coffee table produced by Meising Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Meising’s firm is small, and its resources are limited. During any given production
Bagwell Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container
The Foggy Bottom Development Corporation has just purchased a small hotel for conversion to condominium apartments. The building, in a popular area of Washington, D.C., near the U.S. State
The initial simplex tableau on page M7-49 was developed by Tommy Gibbs, vice president of a large cotton spinning mill. Unfortunately, Gibbs quit before completing this important LP application.
Consider the following optimal tableau, where S1 and S2 are slack variables added to the original problem:(a) What is the range of optimality for the contribution rate of the variable X1?(b) What is
A linear program has been formulated and solved. The optimal simplex tableau for this is given at the bottom of this page.(a) What are the shadow prices for the three constraints? What does a zero
Clapper Electronics produces two models of telephone-answering devices, model 102 (X1) and model H23 (X12) Jim Clapper, vice president for production, formulates their constraints as follows:2X1 +
Refer to Table M7.6, which is the optimal tableau for the Flair Furniture Company problem.(a) What are the values of the shadow prices?(b) Interpret the physical meaning of each shadow price in the
Formulate the dual of this LP problem:Maximize profit = 80X1 + 75X2Subject to 1X1 + 3X2 ≤ 42X1 + 5X2 ≤ 8Find the dual of the problem’s dual.
What is the dual of the following LP problem?Maximize profit = 120X1 + 250X2Subject to 12X1 + 20X2 ≥ 50X1 + 3X2 ≥ 4
The accompanying tableau provides the optimal solution to this dual:Maximize profit = 120U1 + 240U2Subject to 2U1 + 2U2 â‰¥ 0.5U1 + 3U2 â‰¥ 0.4What does the corresponding primal problem look
Given the following dual formulation, reconstruct the original primalproblem:
A firm that makes three products and has three machines available as resources constructs the following LP problem:Solve this problem by computer and answer these questions:(a) Before the third
Management analysts at a Fresno laboratory have developed the following LP primal problem:Maximize profit = 23X1 + 18X2Subject to 8X1 + 4X2 â‰¥ 0.54X1 + 6X2 â‰¥ 1159X1 + 4X2 â‰¥ 116This
Refer to Problem M7-45.(a) If this is solved with the simplex algorithm, how many constraints and how many variables (including slack, surplus, and artificial variables) would be used?(b) If the dual
The Flair Furniture Company first described in Chapter 7, and again in this chapter, manufactures inexpensive tables (T) and chairs (C). The firmâ€™s daily LP formulation is given asMaximize
A Chicago manufacturer of office equipment is desperately attempting to control its profit and loss statement. The company currently manufactures 15 different products, each coded with a one-letter
What is the difference between a state variable and a decision variable?
Why is transformation important for dynamic programming problems?
What is the shortest route between Rice and Dixieville if the road between Hope and Georgetown is improved and the distance is reduce to 4 miles?
Due to road construction between Georgetown and Dixieville, a detour must be taken through country roads (Figure). Unfortunately, this detour has increased the distance from Georgetown to Dixieville
The Rice brothers have a gold mine between Rice and Brown. In their zeal to find gold, they have blown up the road between Rice and Brown. The road will not be in service for five months. What should
The Rice brothers (Figure) wish to determine the potential savings from using the shortest route from Rice to Dixieville rather than just randomly selecting any route. Use dynamic programming to find
Solve the shortest-route problem for the network shown inFigure.
Solve the shortest-route problem for the network shown inFigure.
Leslie Bessler must travel from her hometown to Denver to see her friend Austin. Given the road map of Figure, what route will minimize the distance that Leslie travels?
An air cargo company has the shipping requirements shown in the accompanying table. Two planes are available with a total capacity of 11 tons. How many of each item should be shipped to maximize
Because of a new manufacturing and packaging procedure, the weight of item 2 in Problem M2-14 can be cut in half. Does this change the number or types of items that can be shipped by the air
What is the shortest route through the network inFigure?
Refer to Problem M2-16. The road between node 6 and node 11 is no longer in service due to construction. What is the shortest route, given this situation?
In Problem M2-16, what is the shortest distance from node 6 to the ending node? How does this change if the road between node 6 and node 11 is no longer in service?
1. What do you recommend that Judson do?2. If the total available capacity were 20 tons, how would this change Judson’s decision?Like many other trucking operations, United Trucking got started
The Jessie Cohen Clothing Group owns factories in three towns (W, Y and Z) which distribute to three Cohen retail dress shops (in A, B, and C). Factory availabilities, projected store demands, and
Find the optimal solution to the Jessie Cohen Clothing Group transportation problem (see Problem 9-49).
The personnel director of Dollar Finance Corp. must assign three recently hired college graduates to three regional offices. The three new loan officers are equally well qualified, so the decision
The Orange Top Cab company has a taxi waiting at each of four cab stands in Evanston, Illinois. Four Customers have called and requested service. The distances, in miles, from the waiting taxis to
The Burlington Police Department has five detective squads available for assignment to five open crime cases. The chief of detectives wishes to assign the squads so that the total time to conclude
The G. Saussy Manufacturing company is putting out four new electronic components. Each of Saussy's four plants has the capacity to add one more product to its current line of electronic parts. The
Develop a northeast corner rule for developing an initial solution to a transportation problem. Explain how this would work. Set up an initial solution to the Executive Furniture Corporation problem
In rural west Texas, there are six farms (numbered 1 €“ 6) connected by small roads. The distances in miles between the farms are given in the following table.What is the minimum distance
The farmers in Problem 11-37 have decided to install cable for television and Internet connections. What is the minimum amount of cable required to connect all 6 farms?
A seventh farmer wants to join the group of six in Problem 11-38. The distance of this farm is 8 miles from farm 4, 9 miles from farm 5, and 5 miles from farm 6. What is the minimum amount of cable
Bill Blackstone (Section 11.3), the city manager of Waukesha, Wisconsin has decided to widen the road from node 4 to node 6 so that the capacity in each direction is 3. Find the maximum flow node 1
One hundred years ago, a high plains area near the continental divide in Colorado was used as a working ranch. The views were majestic, although the winters could be harsh. As a result of the boom in
Zuckerman Wiring and Electric is a company that installs wiring and electrical fixtures in residential construction. John Zuckerman has been concerned with the amount of time that it takes to
John Zuckerman would like to determine the total project completion time and the critical path for installing electrical wiring and equipment in residential houses. See Problem 12-32 for details. In
What is the probability that Zuckerman will finish the project described in Problems 12-32 and 12-33 in 40 days or less?
Software Development Specialists (SDS) is involved with developing software for customers in the banking industry. SDS breaks a large programming project into teams that perform the necessary steps.
Sager Products has been in the business of manufacturing and marketing toys for toddlers for the past two decades. Jim Sager, president of the firm, is considering the development of a new
Jim (Problem) has just determined that Activity D has already been completed and that no additional work is required. What is the impact of this change on the activities along the critical path?
Jim (Problem) has just determined that both Activity D and Activity I have been completed. What is the impact of this on the critical path and the total project completion time?
What would happen in Problem if the immediate predecessor activity changed? For example, activity F may have an immediate predecessor of activity A instead of activity B.
Sal's International Barbershop is a popular haircutting and styling salon near the campus of the University of New Orleans. Four barbers work full-time and spend an average of 15 minutes on each
The medical director of a large emergency clinic faces a problem of providing treatment for patients who arrive at different rates during the day. There are four doctors available to treat patients
Buster's Burger is a hamburger restaurant where customers form a single line for the one cashier. The average number of arrivals is 1 per minute and the Poisson distribution accurately defines this
Customers arrive at a corner grocery store at a rate of 3 per minute and the Poisson distribution accurately defines this rate. A single cashier works at the store, and the average time to serve a
A second cashier is added to the grocery store in Problem 13-37, and this cashier works at the same rate as the original one. Assume the arrival rate does not change.(a) What is the average length of
Pantry Shopper is a supermarket in suburban Philadelphia, where competition among supermarkets is fierce. Pantry Shopper management feels that because prices are so competitive, shoppers will choose
What is a two-person, zero-sum game?
How do you compute the value of the game?
What is a pure strategy?
What is a mixed game, and how is it solved?
Determine each playerâ€™s strategy and the value of the game, given the followingtable:
What is the value of the followinggame?
Player A has a $1 bill and a $20 bill, and player B has a $5 bill and a $10 bill. Each player will select a bill from the other player without knowing what bill the other player selected. If the
Resolve Problem M4-12. If the total of the bills is even, player A gets both of the bills selected, but if the total is odd, player B gets both bills.
Solve the followinggame:

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