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…
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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…
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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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