Assignment:
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 (x2), personal interviews during the day (x3), and personal interviews at night (x4) 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.