CHEGG TERMS SAY YOU CAN ANSWER UP TO 4 SUBQUESTIONS, THIS IS 4 SUBQUESTIONS, YOU WILL RECIVE DOUBLE UPVOTE IF YOU DO THIS ORIGINALLY WITH NO COPYING AND CORRECTLY.
12. A new hospital is to be built in a particular location. Restricting attention to just one section of the hospital, the maternity wing, imagine that the following information has been obtained: For the population that the hospital is intended to serve, we may expect an average of twelve deliveries per day. Recovery rooms are no problem. If necessary, rooms out- side the maternity wing can be used. Delivery rooms are also not a problem because they are used only briefly for the actual delivery. The potential bottleneck is the availability of labor rooms. The average time that a labor room will be occupied by a patient is three and a half hours, but of course there is considerable variability in this time. Preparation of a room for the next patient can be accomplished in half an hour, if necessary. If all the labor rooms are occupied, an arriving maternity patient will be directed to another hospital. This is done very reluctantly, but state laws necessitate such action. a. Provide a formula for the fraction of maternity patients who are turned away, as a function of the number of labor rooms designed into the hospital. b. Provide a formula for the occupancy rate of the labor rooms, that is, the long-term average fraction occupied. (This figure is to be multiplied by the room rate to predict annual income from the labor rooms.) c. Formulate a reasonable optimization problem, the solu- tion to which would indicate the appropriate number of labor rooms to provide. (Introduce whatever cost param- eters and the like that you believe are needed.) d. Suppose that additional data were to reveal that the stand- ard deviation of the labor room occupancy time is one hour. What effect would this information have on your analysis? 12. A new hospital is to be built in a particular location. Restricting attention to just one section of the hospital, the maternity wing, imagine that the following information has been obtained: For the population that the hospital is intended to serve, we may expect an average of twelve deliveries per day. Recovery rooms are no problem. If necessary, rooms out- side the maternity wing can be used. Delivery rooms are also not a problem because they are used only briefly for the actual delivery. The potential bottleneck is the availability of labor rooms. The average time that a labor room will be occupied by a patient is three and a half hours, but of course there is considerable variability in this time. Preparation of a room for the next patient can be accomplished in half an hour, if necessary. If all the labor rooms are occupied, an arriving maternity patient will be directed to another hospital. This is done very reluctantly, but state laws necessitate such action. a. Provide a formula for the fraction of maternity patients who are turned away, as a function of the number of labor rooms designed into the hospital. b. Provide a formula for the occupancy rate of the labor rooms, that is, the long-term average fraction occupied. (This figure is to be multiplied by the room rate to predict annual income from the labor rooms.) c. Formulate a reasonable optimization problem, the solu- tion to which would indicate the appropriate number of labor rooms to provide. (Introduce whatever cost param- eters and the like that you believe are needed.) d. Suppose that additional data were to reveal that the stand- ard deviation of the labor room occupancy time is one hour. What effect would this information have on your analysis
