Answer to Question #175714 in Operations Research for Moni

Question

A marketing firm has contracted to do a survey on a political issue for a Spokane television station. The firm conducts interviews during the day and at night, by telephone and in person. Each hour an interviewer works at each type of interview results in an average number of interviews. In order to have a representative survey, the firm has determined that there must be at least 400 day interviews, 100 personal interviews, and 1,200 interviews overall. The company has developed the following linear programming model to determine the number of hours of telephone interviews during the day (x1), telephone interviews at night personal interviews at night (x4) (x2), personal interviews during the day (x3), and that should be conducted to minimize cost:

minimize Z = 2x1 + 3x2 + 5x3 + 7x4 (cost, $)

subject to :

10x1 + 4x3 >= 400 (day interviews)

4x3 + 5x4 >= 100 (personal interviews)

x1 + x2 + x3 + x4 >= 1,200 (total interviews)

x1, x2, x3, x4 >= 0

Solve this model using the simplex method.

Answer 1

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