The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certainbuildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that eachbuilding is cleaned. The management science department formulated the following linear programming model to help with theselection process.Min 210x1 + 200x2+300x3+ 250x4 + 260x5 + 240x6 + 260x7 + 290xgs.t. x1 + x2 + x5 + x7 2 1 (Building A constraint}x1 + x2 + x3 2 1(Building B constraint)X6 + x8 2 1{Building C constraint}x1 + X4 + x7 2 1{Building D constraint}x2 + x7 2 1(Building E constraint)x3 + xg 2 1{Building F constraint}x2 + x5 + X7 2 1(Building G constraint}x1 + X4 + X6 1{Building H constraint)x1 + X4 + x8 2 1(Building I constraint)x1 + x2 + x7 2 1(Building J constraint}J 1, if crew j is selected0, otherwiseSet up the problem in Excel and find the optimal solution.a. What is the cost of the optimal crew assignment?Cost of optimal crew assignmentb. Which crews are assigned to work?< Prev1 of 5Next

Objective Functions and Constraints: Based on the given details, the objective…

Answered: The university is scheduling cleaning…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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A paper-making company has five machines that can produce four different types of papers. The company wants to assign each paper type to separate machines to minimize the total time required. The manufacturing times in minutes per unit of paper produced is listed below: Paper Type Machine Type A B C D M1 2.40 1.60 3.20 3.20 M2 2.10 2.40 3.20 4.50 M3 1.90 1.70 2.60 5.10 M4 2.50 2.50 3.20 6.50 M5 3.25 2.40 3.10 3.60 What is the optimal minimum time?
Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard.Management is considering two varieties of white grapes for the new vineyard: Chardonnayand Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine,and the Riesling grapes would be used to produce a semidry Riesling wine. It takes approximatelyfour years from the time of planting before new grapes can be harvested. Thislength of time creates a great deal of uncertainty concerning future demand and makes thedecision about the type of grapes to plant difficult. Three possibilities are being considered:Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes.Seneca management decided that for planning purposes it would be adequate to consideronly two demand possibilities for each type of wine: strong or weak. With two possibilitiesfor each type of wine, it was necessary to assess four probabilities. With the help of someforecasts in industry…
Daniel Glaser, chairman of the College of San Antonio's business department, needs to assign professors to courses next semester. As a criterion for judging who should teach each course, Professor Glaser reviews the past 2 years' teaching evaluations (which were filled out by students). Since each of the four professors taught each of the four courses at one time or another during the 2-year period, Glaser is able to record a course rating for each instructor. These ratings are shown in the following table. Professor W.W. Fisher D. Golhar Z. Hug N. K. Rustagi a) The optimal assignment of courses to professors that will maximize the overall teaching rating is: Statistics 65 90 70 85 Statistics Management Finance Economics Course Management 75 65 60 40 → Finance 70 95 80 80 The overall teaching rating of the assignment = (enter your response as a whole number). b) The school does not want Professor Fisher to be assigned to the statistics class. Based on the assignment above, a change to…
Fowle Marketing Research, Inc. is faced with the problem of assigning three available project leaders (agents) to each of three new research studies (tasks). Fowle’s management realizes, however, that the time required to complete each study will depend on the experience and ability of the project leader assigned to the study. Since the three studies have been judged to have approximately the same priority, the company would like to determine the assignments that will minimize the total number of days required to complete all three. If a project leader is to be assigned to one and only one client, what assignments should be made (optimal solutions)? How many days are required (objective function value).With three project leaders and three clients, there are total of nine possible assignment alternatives. The alternatives and the estimated project completion times in days are summarized in Table Client Project Leader 1 2…
A manufacturing company must assign machine operators to each of four jobs. The time an operator takes to accomplish the job varies depending on their individual abilities. The table below shows the time in minutes it takes each operator to perform each job. Let's say you ran solver to find optimal assignments that minimized the total labor time, In minutes, what would be the objective function value? Job (Time in Minutes) Worker 6. 5. 3 8. 4 8. 4. 4 5. Worker 3\ 8. 4. 4. C 8 4. D 7. 4 O 16 O 17 O 18 04 O 20
Six ships are docked in a harbor awaiting unloading. The times required to unload the ships are random variables with respective means of 0.6, 1.2, 2.5, 3.5, 0.4, and 1.8 hours. The ships are given a priority weighting based on tonnage. The respective tonnages are 12, 18, 9, 14, 4, and 10. In what sequence should the ships be unloaded in order to minimize the expected weighted time?
The director of a large public library must schedule employees to reshelf books and periodicals checked out of the library. The number of items checked out will determine the labor requirements. The following data reflect the number of items checked out of the library for the past three years: Year 1 1.804 2.711 2,509 2.432 2,468 2,378 2,175 2,445 1,908 1.922 Year 2 2,056 2,321 2,442 2,088 2,694 2,122 2,206 1,869 2,489 2,291 2,352 2,189 Year 3 1,976 2,564 2,616 2,150 2,195 2,663 2,011 1,678 1,778 2,065 2,158 2,440 Month January February March April May June July August September October 2,417 2.274 November December The director needs a time-series method for forecasting the number of items to be checked out during the next month. Suppose that the director considers the best forecast to be the one that minimizes the absolute value of mean bias (Ē). Find the best simple moving average forecast you can using the director's criteria. Using the director's criteria, the best forecast for…
Ensemble Theatre of Cincinnati D. Lynn Meyers has been Producing Artistic Director of the nationally renowned Ensemble Theatre of Cincinnati (ETC) since 1995. The nonprofit ETC, recently celebrating its 25th anniversary, is dedicated to the production and development of new plays and of works new to the region. Lynn values the opinions of each member of her small staff when hiring. She usually interviews four or five people for a staff position and conducts two interviews. After the preliminary interview determines that an applicant is suitable, she says, “We invite the person back to meet the staff they would have contact with on a daily basis.” She has passed on qualified candidates who did not interact well with their prospective coworkers or who did not convince her that they had a strong desire for the job. Lynn researches job applicants online and on social media sites. “Frankly, if we find unprofessional behavior, we take that into consideration,” she says. “We always check…
The manager of a medical center wants to schedule staff based on a pattern of 5 days working and 2 consecutive days off. Based on the history of their workload, below is their weekly staff requirement: Thursday Day Staff needed Monday 6 O Saturday and Sunday Monday and Friday Tuesday and Thursday Wednesday and Friday Tuesday 5 a. Determine what days employee 3 does not need to work. Wednesday 4 Minimum number of full time staff b. Determine the minimum number of full time staff. Friday Saturday 6 4 Sunday 3
KrazySockzThe KrazySockz Company is known for their colorful yetcomfortable socks. They have forecasted their demand for the nextsix months as follows: Month 1 demand is 30,000, month 2demand is 50,000, month 3 demand is 20,000, month 4 demand is10,000, month 5 demand is 15,000 and month 6 demand is 20,000.At the beginning of month 1 they have 15,000 pairs of socks onhand. KrazySockz currently has 40 production employees. Each productionemployee costs the company the company $4,000 per month ($3,200 salary and $800in other costs) per month. Production employees can work up to 160 hours permonth before they must be paid overtime. Overtime is paid at a rate of $30 per hourand production employees can not work more than 30 hours per month overtime. Ittakes 15 minutes of labor and $0.75 of raw material to produce a pair of socks.KrazySockz can hire or fire employees each month. Hiring a production employeeincurs a cost of $3,500 and firing a production employee costs $4,500. At the end…
I want to know the solution to this problem done by excel solver!
Use the simplex iteration method each of the objective function using the same constrains Maximize Z=3X1-X2+3X3+4X4 Minimize Z=5x1-4x2+6x3-8x4 Constrains x1+2x2+2x3+4x4=<40 2x1-x2+x3+2x4=<8 4x1-2x2+x3-x4=<10 x1, x2, x3, x4=>0

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