ing to meet 55. MARKET RESEARCH Trendex, a telephone survey company, has been hired to conduct a television-viewing poll among urban and suburban families in the Los Angeles area. The client has stipulated that a maximum of 1500 families is to be interviewed. At least 500 urban families must be inter- viewed, and at least half of the total number of families interviewed must be from the suburban area. For this ser- vice, Trendex will be paid $6000 plus $8 for each com- pleted interview. From previous experience, Trendex has determined that it will incur an expense of $4.40 for each successful interview with an urban family and $5 for each successful interview with a suburban family. How many 61 urban and suburban families should Trendex interview to maximize its profit? What is the optimal profit? 56. PRODUCTION SCHEDULING Bata Aerobics manufactures two models of steppers used for aerobic exercises. Manufac- turing each luxury model requires 10 lb of plastic and 10 min of labor. Manufacturing each standard model requires 16 lb of plastic and 8 min of labor. The profit for each luxury model is $40, and the profit for each standard model is $30. If 6000 lb of plastic and 60 labor-hours are available for the production of the steppers per day, how many steppers of each model should Bata produce each day to maximize its profit? What is the optimal profit? n Exercises 57-59, determine whether the statement is true or alse. If it is true, explain why it is true. If it is false, give an exam- le to show why it is false. 7. An optimal solution of a linear programming problem is a feasible solution, but a feasible solution of a linear pro- gramming problem need not be an optimal solution. 02, ounces of each brand of dog food ing to meet the given requirements at a minimum cost. 55. MARKET RESEARCH Trendex, a telephone survey company, has been hired to conduct a television-viewing poll among urban and suburban families in the Los Angeles area. The client has stipulated that a maximum of 1500 families is to be interviewed. At least 500 urban families must be inter- viewed, and at least half of the total number of families interviewed must be from the suburban area. For this ser- vice, Trendex will be paid $6000 plus $8 for each com- pleted interview. From previous experience, Trendex has determined that it will incur an expense of $4.40 for each successful interview with an urban family and $5 for each successful interview with a suburban family. How many urban and suburban families should Trendex interview tO 6. maximize its profit? What is the optimal profit? 56. PRODUCTION SCHEDULING Bata Aerobics manufactures two models of steppers used for aerobic exercises. Manufac- turing each luxury model requires 10 lb of plastic and 10 min of labor. Manufacturing each standard model requires 16 lb of plastic and 8 min of labor. The profit for each luxury model is $40, and the profit for each standard model is $30. If 6000 lb of plastic and 60 labor-hours are available for the production of the steppers per day, how many steppers of each model should Bata produce each day to maximize its profit? What is the optimal profit? Exercises 57-59, determine whether the statement is true a se. If it is true, explain why it is true. If it is false, give an exa to show why it is false. An optimal solution of a linear programming problem feasible solution, but a feasible solution of a linear pre gramming problem need not be an optimal solution.