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Chapter: 16 -Problem: 42 >> The Research and Development Division of the Emax ­Corporation has developed three new products. A decision now needs to be made on which mix of these products should be produced. Management wants primary consideration given to three factors: total profit, stability in the workforce, and achieving an increase in the company’s earnings next year from the $75 million achieved this year. In particula
Answer Preview: To begin, we need to define the variables we will use in our model. Let's define the variables as follows: $x_1$: The production rate of Product 1. $…

, Chapter: 4 -Problem: 37 >> Consider the following problem.MaximizeZ = 4 x1 + 2 x2 + 3 x3 + 5 x4, subject to Introduce artificial variables to reformulate this problem as a convenient artificial problem for preparing to apply the simplex method. Transcribed Image Text: 2x + 3x? + 4x3 + 2x? = 300 8x? + x? + x3 + 5x? = 300 and x
Answer Preview: Maximize Z = 4 x1 + 2 x2 + 3 …

, Chapter: 3 -Problem: 32 >> The Southern Confederation of Kibbutzim is a group of three kibbutzim (communal farming communities) in Israel. Overall planning for this group is done in its Coordinating Technical Office. This office currently is planning agricultural production for the coming year.The agricultural output of each kibbutz is limited by both the amount of available irrigable land and the quantity of water allocate
Answer Preview: (a) The objective in this problem is to maximize the total net return of the Southern Co…

, Chapter: 20 -Problem: 31 >> Let r1, r2, . . . , rn be uniform random numbers. Define xi = ? ln ri and yi = ? ln (1 ? ri), for i = 1, 2, . . . , n, and Label each of the following statements as true or false, and then justify your answer.(a) The numbers x1, x2, . . . , xn and y1, y2, . . . , yn are random observations from the same exponential distribution.(b) The average of x1, x2, . . . , xn is equal to the average of y1, y
Answer Preview: (a) This statement is false because the random variables xi, i = 1, 2, . . . , n h…

, Chapter: 3 -Problem: 37 >> United Airways is adding more flights to and from its hub airport, so it needs to hire additional customer service agents. However, it is not clear just how many more should be hired. Management recognizes the need for cost control while also consistently providing a satisfactory level of service to customers. Therefore, an OR team is studying how to schedule the agents to provide satisfactory ser
Answer Preview: Solution: (a) Let the variables xij denote the number of agents assigned to shift i and let xij+1 be …

, Chapter: 3 -Problem: 5 >> The manager of an automobile assembly plant must make decisions about the production schedule for her two types of car models next month. Several factors need to be considered, including a limited number of labor-hours, different numbers of labor-hours needed for each of the two car models, a limited number of car doors available from the door supplier, and a limited demand for one of the car mode
Answer Preview: Answer; The manager must determine (1) the number of cars that can be sold with a given number of la…

, Chapter: 16 -Problem: 43 >> Reconsider the original version of the Dewright Co. problem summarized in Table 16.8 . After further reflection about the solution obtained by the simplex method, management now is asking some what-if questions.Table 16.8(a) Management wonders what would happen if the penalty weights in the rightmost column of Table 1 were to be changed to 7, 4, 1, and 3, respectively. Would you expect the optimal
Answer Preview: (a) If the penalty weights in the rightmost column of Table 16 8 were changed to 7, 4, 1, and 3, res…

, Chapter: 16 -Problem: 44 >> One of the most important problems in the field of statistics is the linear regression problem. Roughly speaking, this problem involves fitting a straight line to statistical data represented by points — (x1, y1), (x2, y2), . . . , (xn, yn) — on a graph. If we denote the line by y = a + bx, the objective is to choose the constants a and b to provide the “best” fit according to some criterion. The
Answer Preview: A linear programming model for this problem is : This is …

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, Chapter: 16 -Problem: 40 >> One of management’s goals in a goal programming problem is expressed algebraically as 3x1 + 4x2 + 2x3 = 60, where 60 is the specific numeric goal and the left-hand side gives the level achieved toward meeting this goal.(a) Letting y + be the amount by which the level achieved exceeds this goal (if any) and y? the amount under the goal (if any), show how this goal would be expressed as an equality
Answer Preview: (a) This goal would be expressed as an equality constraint when reformulating the prob…

, Chapter: 16 -Problem: 41 >> Management of the Albert Franko Co. has established goals for the market share it wants each of the company’s two new products to capture in their respective markets. Specifically, management wants Product 1 to capture at least 15 percent of its market and Product 2 to capture at least 10 percent of its market. Three advertising campaigns are being planned to try to achieve these market shares. On
Answer Preview: a. Formulate a goal programming model for this problem: …

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