SOLVE QUESTIONS 1-10

PROBLEM 2 p. 299 example 8.3 in the textbook Sequoia Clinic is a private hospital that has a fluctuating demand for nursing care, since some days typically have higher admissions of patient than others. Management of the Clinic is trying to set up a work schedule for full time nurses that will allow them two consecutive days off each week. Clinic can also hire part-time nurses who will work a Friday-Sunday-Monday schedule. Daily pay for a full-time nurse is $120, except for Saturdays and Sundays when they earn $150 and $180 respectively. Part-time nurses earn $240 per 3-day workweek. The minimum required number of nurses on duty each day of the week is given in table below. Monday 17 Subject to 3883385 Tuesday Wednesday Thursday 14 15 C1 12 A cost-minimizing model to determine the number of full-time nurses that should start their workweek each day of the week and the number of part-time nurses that should be hired is formulated and solved below. The following decision variables are used: MON, TU, WED, TH, FR, SA, SU = the number of full-time nurses who start 5 consecutive day shifts on Monday, Tuesday, etc., respectively P = the number of part-time nurses who work a Friday-Sunday-Monday schedule. C7 Friday 22 Min Z- 600MON+630TU+690WED + 690TH+690FR + 690SA+660SU + 240P Saturday 10 Sunday 15 1MON + 1TH+1FR+1SA + 1SU + 1P>= 17 IMON + ITU + 1FR + 1SA +1SU >= 14 IMON+1TU+1WED + 1SA + 1SU >= 12 IMON+ 1TU +1WED + 1TH + 1SU >= 15 IMON + ITU +1WED + 1TH+1FR + 1P >= 22 ITU +1WED + 1TH+1FR +1SA >= 10 1WED+ 1TH+1FR + 1SA +1SU+1P >= 15 Monday requirement Tuesday requirement Wednesday requirement Thursday requirement Friday requirement Saturday requirement Sunday requirement

***** POM Program Output "***. Z=12180.000 Objective Coefficient Ranges Right Hand Side Ranges QUESTIONS FOR SEQUOLA CLINIC (treat each question independently) 1) What is the minimum cost of staffing the clinic for one week? 2) How many full-time and how many part-time nurses are required? 3) On which day of the week the minimum number of nurses required was exceeded? By how many? 4) By how much can the wages of part-time nurses increase without their affecting the optimal solution? 5) If you could recuce admissions on one of the days of the week so that this day's nurse requirement would be reduced, on which day should you attempt to do it? Why? 6) If you could shift admissions from one day to another and thus reduce stuffing requirement from one day to another, what day's requirement you would attempt to reduce and what day's requirement you would attempt to increase? Explain why. What affect, if any, will the change have on weekly cost? 7) If you could cut the daily pay for those full-tume nurses who's 5 -day work week does not include either Saturday or Sunday by $10 per day, how would this affect the weekly cost of staffing the clinic? Would the optimal staffing schedule change? 8) If one of the part-time nurses called in and informed the hospital that she is not able to work on Friday, but will be working her Monday and Sunday schedule. Will the hospital be able to meet the daily requirement without changing the staffing schedule? Explain why or why not. How does the weekly cost change? 9) Suppose you would like to reduce the weekly pay for those nurses who start their 5-day work week on Thursday and Sunday by of $20 and $10 respectrvely. Would this affect your optimal staffing schedule? What about the weekly cost? 10) You can reduce the weekly pay for full-time nurses by $20, but only for one tops of shift, ie. you could give this reduction to either to all nurses who start on Monday, or to all nurses who start on Tuesday, .... etc, or to all nurses who start on Sunday. Where should you reduce the wages then? Explain why PROBLEM 2 p. 299 example 8.3 in the textbook Sequoia Clinic is a private hospital that has a fluctuating demand for nursing care, since some days typically have higher admissions of patient than others. Management of the Clinic is trying to set up a work schedule for full time nurses that will allow them two consecutive days off each week. Clinic can also hire part-time nurses who will work a Friday-Sunday-Monday schedule. Daily pay for a full-time nurse is $120, except for Saturdays and Sundays when they earn $150 and $180 respectively. Part-time nurses earn $240 per 3-day workweek. The minimum required number of nurses on duty each day of the week is given in table below. A cost-minimizing model to determine the number of full-time nurses that should start their workweek each day of the week and the number of part-time nurses that should be hired is formulated and solved below. The following decision variables are used: MON, TU, WED ,TH,FR,SA,SU = the number of full-time nurses who start 5 consecutive day shifts on Monday, Tuesday, etc, respectively P= the number of part-time nurses who work a Friday-Sunday-Monday schedule. Min Z=600MON+630TU+690WED+690TH+690FR+690SA+660SU+240P Subject to C1C2C3C4C5C6C71MON+1TH+1FR+1SA+1SU+1P>=171MON+1TU+1FR+1SA+1SU>=141MON+1TU+1WED+1SA+1SU>=121MON+1TU+1WED+1TH+1SU>=151MON+1TU+1WED+1TH+1FR+1P>=221TU+1WED+1TH+1FR+1SA>=101WED+1TH+1FR+1SA+1SU+1P>=15MondayrequirementTuesdayrequirementWednesdayrequirementThursdayrequirementFridayrequirementSaturdayrequirementSundayrequirement Monday requirement Tuesday requirement Wednesday requirement Thursday requirement Friday requirement Saturday requirement Sunday requirement