Questions and Answers of Introduction To Operations Research

Consider the Z*() function shown in Fig. 7.1 for parametric linear programming with systematic changes in the cj parameters.(a) Explain why this function is piecewise linear.(b) Show that this
Consider Prob. 6.7-2.Use parametric linear programming to find an optimal solution as a function of over the following ranges of.(a) 0 20.(b) 20 0. (Hint: Substitute for, and then increase from
Use parametric linear programming to find an optimal solution for the following problem as a function of, for 0 30.Maximize Z() 5x1 6x2 4x3 7x4, subject to 3x1 2x2 x3 3x4 135 2 2x1
Use the parametric linear programming procedure for making systematic changes in the bi parameters to find an optimal solution for the following problem as a function of, for 025.Maximize Z() 2x1
Consider the following problem.Maximize Z() (10 )x1 (12 )x2 (7 2)x3, subject to x1 2x2 2x3 30 x1 x2 x3 20 and x1 0, x2 0, x3 0.I (a) Use parametric linear programming to find an
Use parametric linear programming to find the optimal solution for the following problem as a function of, for 0 20.Maximize Z() (20 4)x1 (30 3)x2 5x3, subject to 3x1 3x2 x3 30 8x1
Consider the following problem.Maximize Z 8x1 24x2, subject to x1 2x2 10 2x1 x2 10 and x1 0, x2 0.Suppose that Z represents profit and that it is possible to modify the objective function
Use the dual simplex method manually to reoptimize for each of these two cases, starting from the revised final tableau.
Consider parts (a) and (b) of Prob.
Consider the example for case 1 of sensitivity analysis given in Sec. 6.7, where the initial simplex tableau of Table 4.8 is modified by changing b2 from 12 to 24, thereby changing the respective
Consider the following problem.Maximize Z 3x1 2x2, subject to 3x1 x2 12 x1 x2 6 5x1 3x2 27 and x1 0, x2 0.I (a) Solve by the original simplex method (in tabular form). Identify the
Use the dual simplex method manually to solve the following problem.Minimize Z 7x1 2x2 5x3 4x4, subject to 2x1 4x2 7x3 x4 5 8x1 4x2 6x3 4x4 8 3x1 8x2 x3 4x4 4 and xj 0, for
Use the dual simplex method manually to solve the following problem.Minimize Z 5x1 2x2 4x3, subject to 3x1 x2 2x3 4 6x1 3x2 5x3 10 and x1 0, x2 0, x3 0.
Consider the following problem.Maximize Z x1 x2, subject to x1 x2 8 x2 3x1 x2 2 and x1 0, x2 0.(a) Solve this problem graphically.(b) Use the dual simplex method manually to solve this
Read the article footnoted in Sec. 2.1 that describes an OR study done for the San Francisco Police Department.(a) Summarize the background that led to undertaking this study.(b) Define part of the
Read the article footnoted in Sec. 2.1 that describes an OR study done for the Health Department of New Haven, Connecticut.(a) Summarize the background that led to undertaking this study(b) Outline
Read the article footnoted in Sec. 2.2 that describes an OR study done for the Rijkswaterstaat of the Netherlands. (Focus especially on pp. 3–20 and 30–32.)(a) Summarize the background that led
Refer to pp. 18–20 of the article footnoted in Sec. 2.2 that describes an OR study done for the Rijkswaterstaat of the Netherlands. Describe an important lesson that was gained from model
Read the article footnoted in Sec. 2.5 that describes an OR study done for Texaco.(a) Summarize the background that led to undertaking this study.(b) Briefly describe the user interface with the
Refer to the article footnoted in Sec. 2.5 that describes an OR study done for Yellow Freight System, Inc.(a) Referring to pp. 147–149 of this article, summarize the background that led to
Refer to pp. 163–167 of the article footnoted in Sec. 2.5 that describes an OR study done for Yellow Freight System, Inc., and the resulting computer system SYSNET.(a) Briefly describe how the OR
Read the article footnoted in Sec. 2.4 that describes an OR study done for IBM and the resulting computer system Optimizer.(a) Summarize the background that led to undertaking this study.(b) List the
Read Selected Reference 3. The author describes 13 detailed phases of any OR study that develops and applies a computer-based model, whereas this chapter describes six broader phases. For each of
Consider the following objective function for a linear programming model:Maximize Z 2x1 3x2(a) Draw a graph that shows the corresponding objective function lines for Z 6, Z 12, and Z 18.(b) Find
Use the graphical method to solve the problem:Maximize Z 2x1 x2, subject to x2 10 2x1 5x2 60 x1 x2 18 3x1 x2 44 and x1 0, x2 0.
Use the graphical method to solve the problem:Maximize Z 10x1 20x2, subject tox1 2x2 15 x1 x2 12 5x1 3x2 45 and x1 0, x2 0.
The Whitt Window Company is a company with only three employees which makes two different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. They earn$60 profit for each
The Apex Television Company has to decide on the number of 27- and 20-inch sets to be produced at one of its factories.Market research indicates that at most 40 of the 27-inch sets and 10 of the
The Omega Manufacturing Company has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting
Consider the following problem, where the value of c1 has not yet been ascertained.Maximize Z c1x1 x2, subject to x1 x2 6 x1 2x2 10 and x1 0, x2 0.Use graphical analysis to determine
Consider the following problem, where the value of k has not yet been ascertained.Maximize Z x1 2x2, subject tox1 x2 2 x2 3 kx1 x2 2k 3, where k 0 and x1 0, x2 0.The solution
Consider the following problem, where the values of c1 and c2 have not yet been ascertained.Maximize Z c1x1 c2x2, subject to 2x1 x2 11x1 2x2 2 and x1 0, x2 0.Use graphical analysis to
Use the graphical method to find all optimal solutions for the following model:Maximize Z 500x1 300x2, subject to 15x1 5x2 300 10x1 6x2 240 8x1 12x2 450 and x1 0, x2 0.
Use the graphical method to demonstrate that the following model has no feasible solutions.Maximize Z 5x1 7x2, subject to 2x1 x2 1x1 2x2 1 and x1 0, x2 0.
Suppose that the following constraints have been provided for a linear programming model.x1 3x2 303x1 x2 30 and x1 0, x2 0.(a) Demonstrate that the feasible region is unbounded.(b) If
Reconsider Prob.
Use the graphical method to solve this problem:Maximize Z 15x1 20x2, subject to x1 2x2 10 2x1 3x2 6 x1 x2 6 and x1 0, x2 0.
Use the graphical method to solve this problem:Minimize Z 3x1 2x2, subject to x1 2x2 12 2x1 3x2 12 2x1 x2 8 and x1 0, x2 0.
Consider the following problem, where the value of c1 has not yet been ascertained.Maximize Z c1x1 2x2, subject to 4x1 x2 12 x1 x2 2 and x1 0, x2 0.Use graphical analysis to determine
Consider the following model:Minimize Z 40x1 50x2, subject to 2x1 3x2 30 x1 x2 12 2x1 x2 20 and x1 0, x2 0.(a) Use the graphical method to solve this model.(b) How does the optimal
Ralph Edmund loves steaks and potatoes. Therefore, he has decided to go on a steady diet of only these two foods (plus some liquids and vitamin supplements) for all his meals. Ralph realizes that
Dwight is an elementary school teacher who also raises pigs for supplemental income. He is trying to decide what to feed his pigs. He is considering using a combination of pig feeds available from
Larry Edison is the director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 A.M. until midnight. Larry has monitored the usage of
The Fagersta Steelworks currently is working two mines to obtain its iron ore. This iron ore is shipped to either of two storage facilities. When needed, it then is shipped on to the company’s
The Weigelt Corporation has three branch plants with excess production capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants have this capability,
A cargo plane has three compartments for storing cargo:front, center, and back. These compartments have capacity limits on both weight and space, as summarized below:Furthermore, the weight of the
Comfortable Hands is a company which features a product line of winter gloves for the entire family—men, women, and children. They are trying to decide what mix of these three types of gloves to
Slim-Down Manufacturing makes a line of nutritionally complete, weight-reduction beverages. One of their products is a strawberry shake which is designed to be a complete meal. The strawberry shake
Read the article footnoted in Sec. 3.5 that describes the first case study presented in that section: “Choosing the Product Mix at Ponderosa Industrial.”(a) Describe the two factors which,
Read the article footnoted in Sec. 3.5 that describes the second case study presented in that section: “Personnel Scheduling at United Airlines.”(a) Describe how United Airlines prepared shift
Read the 1986 article footnoted in Sec. 2.1 that describes the third case study presented in Sec. 3.5: “Planning Supply, Distribution, and Marketing at Citgo Petroleum Corporation.”(a) What
You are given the following data for a linear programming problem where the objective is to maximize the profit from allocating three resources to two nonnegative activities.(a) Formulate a linear
Ed Butler is the production manager for the Bilco Corporation, which produces three types of spare parts for automobiles.The manufacture of each part requires processing on each of two machines, with
You are given the following data for a linear programming problem where the objective is to minimize the cost of conducting two nonnegative activities so as to achieve three benefits that do not fall
Fred Jonasson manages a family-owned farm. To supplement several food products grown on the farm, Fred also raises pigs for market. He now wishes to determine the quantities of the available types of
Maureen Laird is the chief financial officer for the Alva Electric Co., a major public utility in the midwest. The company has scheduled the construction of new hydroelectric plants 5, 10, and 20
Reconsider Prob. 3.1-11.(a) Use MPL/CPLEX to formulate and solve the model for this problem.(b) Use LINGO to formulate and solve this model.C
Reconsider Prob. 3.4-11.(a) Use MPL/CPLEX to formulate and solve the model for this problem.(b) Use LINGO to formulate and solve this model.C
Reconsider Prob. 3.4-15.(a) Use MPL/CPLEX to formulate and solve the model for this problem.(b) Use LINGO to formulate and solve this model.C
Reconsider Prob. 3.4-18.(a) Use MPL/CPLEX to formulate and solve the model for this problem.(b) Use LINGO to formulate and solve this model.C
Reconsider Prob. 3.6-4.(a) Use MPL/CPLEX to formulate and solve the model for this problem.(b) Use LINGO to formulate and solve this model.C
Reconsider Prob. 3.6-5.(a) Use MPL/CPLEX to formulate and solve the model for this problem.(b) Use LINGO to formulate and solve this model.
In concept development, you select a given style of service: counter tray, cart, arm, or French. Which will fit your concept best, and why? LO-6
Roughly what percentage of meals eaten out are purely for pleasure? LO-6
What is the relationship between your logo and your restaurant concept? LO-6
Suppose your name is Joe Smith. Would you have any legal problem naming your restaurant Smith’s? LO-6
Comment on the statement ‘‘Behind every restaurant there is a concept.’’ LO-6
List five factors that together help formulate a restaurant concept. LO-6
How are restaurant image and concept related? LO-6
In what way do several existing restaurants close to a site affect the desirability of that site for another restaurant? LO-6
Can a particular site be wrong for one restaurant, right for another? Explain. LO-6
The desirability of a given restaurant location changes with time. Give three reasons why this is true. LO-6
What location criteria would you suggest for a restaurant featuring diet foods? LO-6
What colors would you suggest for a high-style Italian restaurant? LO-6
A luxury, white-tablecloth restaurant has a rheostatic lighting control. How would you use it and for what purposes?
Why or why not would you use upholstered soft seating in a quick-service restaurant? LO-6
What kind of restaurant location can exist without parking? LO-6
In building a restaurant, what amount of money should you expect to invest per seat? LO-6
Suppose you have $80,000 with which to start a restaurant and no possibility of borrowing additional capital. What kind of restaurant should you consider and how would you go about getting started?
Go online and look for three chain and three independent restaurant concepts that appeal to you. Share your findings with your class.Go to www.census.gov/ and www.demographicsnow.com to look up the
Identify the major elements of a business plan.
Develop a restaurant business plan.
Conduct a market assessment.
Discuss the importance of the four Ps of the marketing mix.
Describe some promotional ideas for a restaurant.
In your restaurant project, which will be your principal target market?
How will you determine your restaurant’s pricing policy?
Search for information on restaurant business plans—there is no need to use sites that want money. Check the SBA Web site and search for business plans.Share your findings with your class.
Prepare an income statement and a financial budget.
Identify requirements for obtaining a loan in order to start a restaurant.
Discuss the strengths and weaknesses of the various types of loans available to restaurant operators.
List questions and the types of changes a lessee should consider before signing a lease.
In drawing up a sales budget for a casual Italian restaurant, what percentage of weekly sales should be forecasted for Friday and Saturday evenings?
A casual restaurant with a $1 million sales volume should have how many full-time equivalent employees?
In seeking a construction loan, would you expect to have the entire amount of the loan given to you in a lump sum? Explain.
Is it possible (not probable) to start a restaurant without any cash of your own? Explain.
Go to sba.gov and seek information on business start-up finance that will be helpful to your restaurant start-up. Be prepared to share the information with your class.
Describe the various forms of business ownership.
Discuss the advantages and disadvantages of each form of business.
Recognize the legal aspects of doing business.

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