Explanation Given: Trendex has stipulated 1500 families for an interview out of which at least 500 would be of urban families, and half of the families would be of the total suburban families. The Trendex company will get $ 6000 plus $ 8 for each completed interview. From the past experiences, trendex has determined an expense of $ 4.40 with an urban family and $ 5 with a suburban family for each successful interview. Approach: The solution of linear programming problem is as follows. If a linear programming problem has a solution, then it must occur at a vertex or corner point, of the feasible set S associated with the problem. The method to find the corners is as follows. Graph the feasible set and then find the coordinates of all the corner points of the feasible set, then evaluate the objective function at each corner point. Calculation: Let the number of urban families for the interview be x and the number of suburban families for the interview be y . The objective is to attain the maximum profit to Trendex based on the number of urban and suburban families for the interview. Trendex receives the $ 6000 plus $ 8 for each completed interview. Thus, 6000 + 8 ( x + y ) . Also, the expense of $ 4.40 for each successful interview with an urban family and $ 5 for each successful interview with a suburban family is as follows. 4.40 x + 5 y . Therefore, the objective function is, P = 6000 + 8 ( x + y ) − ( 4.40 x + 5 y ) = 6000 + 8 x + 8 y − 4.40 x − 5 y = 6000 + 3.6 x + 3 y . A maximum of 1500 families is to be interviewed. Then, x + y ≤ 1500 . At least 500 urban families are to be interviewed. Then, x ≥ 500 Also, at least half of the families will be of the total suburban families. y ≥ 1 2 ( x + y ) y ≥ 1 2 x + 1 2 y 1 2 y − 1 2 x ≥ 0 y − x ≥ 0 Therefore, the objective function is, Maximize P = 6000 + 3

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 3.3, Problem 53E

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The number of urban and suburban families Trendex interviews to maximize the profit and the amount of optimal profit.

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Chapter 3.3, Problem 52E

Chapter 3.3, Problem 54E

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Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

Ch. 3.1 - Prob. 1CQ Ch. 3.1 - Prob. 2CQ Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - Prob. 6E Ch. 3.1 - In Exercises 110, find the graphical solution to...Ch. 3.1 - In Exercises 110, find the graphical solution to...

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The number of urban and suburban families Trendex interviews to maximize the profit and the amount of optimal profit.

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