ruckleho X HAMAS - Zoom JODY : QBA-362-002 [HIL. FA. chment/HIL. 10122.202310/Assignments/3d9a33a5-0497-4286-996e-021036914e3/QBA%20362%20HW2.pdf 13 100% + 1. Rucklehouse Public Relations has been contracted to do a survey following an election primary in New Hampshire. The firm must assign interviewers to conduct the survey by telephone or in person. One person can conduct 80 telephone interviews or 40 personal interviews in a single day. The following criteria have been established by the firm to ensure a representative survey: . At least 3,000 interviews must be conducted. . At least 1,000 interviews must be by telephone. . At least 800 interviews must be personal. An interviewer conducts only one type of interview each day. The cost is $50 per day for a telephone interviewer and $70 per day for a personal interviewer. The firm wants to know the minimum number of interviewers to hire to minimize the total cost of the survey. Formulate a linear programming model for this problem. Determine the sensitivity ranges for the daily cost of a telephone interviewer and the number of personal interviews required. Does the firm conduct any more telephone and personal interviews than are required, and if so, how many more? What would be the effect on the optimal solution if the firm was required by the client to increase the number of personal interviews conducted from 800 to a total of 1,200? If the firm could reduce the minimum interview requirement for either telephone or personal interviews, which should the firm select? How much would a reduction of one interview in the requirement you selected reduce total cost? Solve the model again, using the computer, with the reduction of this one interview in the constraint requirement to verify your answer. Identify the sensitivity ranges for the cost of a personal interview and the number of total interviews required. W 28 C DELLtachment/HIL. 10122.202310/Assignments/3d9a33a5-0497-4286-996e-021036914e3/QBA%20362%20HW2.pdf 2 /3 100% + 2 . The Southfork Feed Company makes a feed mix from four ingredients-oats, corn, soybeans, and a vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix: . At least 30% of the mix must be soybeans. . At least 20% of the mix must be the vitamin supplement. . The ratio of corn to oats cannot exceed 2 to 1. . The amount of oats cannot exceed the amount of soybeans. . The mix must be at least 500 pounds. A pound of oats costs $0.50, a pound of corn, $1.20, a pound of soybeans, $0.60, and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingredient to put in the mix to minimize cost. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer. 3. Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determine a schedule for nurses to make sure there are enough of them on duty throughout the day. During the day, the demand for nurses varies. Maureen has broken the day into twelve 2-hour periods. The slowest time of the day encompasses the three periods from 12:00 A.M. O Ei WA pound of oats costs $0.50, a pound of corn, $1.20, a pound of soybeans, $0.60, and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingredient to put in the mix to minimize cost. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer. Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determine a schedule for nurses to make sure there are enough of them on duty throughout the day. During the day, the demand for nurses varies. Maureen has broken the day into twelve 2-hour periods. The slowest time of the day encompasses the three periods from 12:00 A.M. to 6:00 A.M., which, beginning at midnight, require a minimum of 30, 20, and 40 nurses, respectively. The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 A.M.-8:00 A.M. period, a minimum of 50, 60, 80, and 80 nurses are required for these four periods, respectively. After 2:00 P.M. the demand for nurses decreases during the afternoon and evening hours. For the five 2-hour periods beginning at 2:00 P.M. and ending at midnight, 70, 70, 60, 50, and 50 nurses are required, respectively. A nurse reports for duty atthe beginning of one of the 2-hour periods and works 8 consecutive hours (which is required in the nurses' contract). Dr. Becker wants to determine a nursing schedule that will meet the hospital's minimum requirements throughout the day while using the minimum number of nurses. a. Formulate a linear programming model for this problem. b. Solve this model by using the computer. O w DELL3 / 3 100% + 4 A jeweler and her apprentice make silver pins and necklaces by hand. Each week they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin and 10 hours of labor and 6 ounces of silver to make a necklace. Each pin also contains a small gem of some kind. The demand for pins is no more than six per week. A pin earns the jeweler $400 in profit, and a necklace earns $100. The jeweler wants to know how many of each item to make each week to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer. Compare this solution with the solution with out integer restrictions, and indicate whether the rounded-down solution would have been optimal. he O DOLL