A college student has 7 days remaining before final examinations begin in her four courses, and she wants to allocate this study time as effectively as possible. She needs at least 1 day on each course, and she likes to concentrate on just one course each day. So she wants to allocate 1, 2, 3, or 4 days to each course. Having recently taken an OR course, she decides to use dynamic programming to make these allocations to maximize the total grade points to be obtained from the four courses. She estimates that the alternative allocations for each course would yield the number of grade points shown in the following table.| Study Days | Estimated Grade Points ||------------|------------------------|| | Course 1 | Course 2 | Course 3 | Course 4 || 1 | 1 | 5 | 4 | 4 || 2 | 3 | 6 | 6 | 4 || 3 | 6 | 8 | 7 | 5 || 4 | 8 | 8 | 9 | 8 |Solve this problem by dynamic programming. (30 points)

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Answered: A college student has 7 days remaining…

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 factory has two stations, station X and station Y. There are two different types of units, flow units A, and flow units B. The table below includes details about how long each unit type spends at each station: Flow Unit A Flow Unit B Station X 6 min 5 min Station Y 15 min 4 min The demand rate: Flow units A: 10 units per hour. Flow units B: 15 units per hour There are 4 machines at station X and 2 machine at station Y. What is the flow rate for unit B?
Modify the machine-to-job assignment model under the assumption that only three of the four jobs must be completed. In other words, one of the four jobs does not have to be assigned to any machine. What is the new optimal solution?
A manufacturing system is used to produce a product.Each unit of product must be processed sequentially through workstations.V -----> W -----> X -----> Y The processing time on each workstation are as follows:Workstation V, 11 minutes per unit,Workstation W, 6 minutes per unit,Workstation X, 19 minutes per unit,Workstation Y, 19 minutes per unit. The raw material is always available in the front of workstation V. The manufacturing system can produce __________ units in 27 hours. Use at least 4 decimals.You must show your calculation steps and brief explanation on your Excel spreadsheets.
Lee Beedo, a hip bachelor in Edmond, has a date for Saturday night and finds himself without a thing to wear. Faced with the daunting task of doing enough laundry to fully accessorize during his night out, Lee has sorted his clothes into loads according to fabric and color. Based on his vast experience doing laundry, Lee knows how long each load will take in both the washer and the dryer. He glances at his watch; it is now 2:00 p.m. and he has to have the last load dry by 8:30 p.m. to be there in time. Help Lee develop a schedule that will enable him to make his date on time and depict that schedule using a Gantt chart. Can he make it and, if so, by how much?
Personnel planning is an important function for many firms. Consider a company’s department with a desired headcount of 100 positions. Suppose that employees leave their positions at a rate of 3.4 per month, and that it requires an average of 4 months for the firm to fill open positions. Analysis of past data shows that the number of employees leaving the firm per month has the Poisson distribution, and that the time required to fill positions follows Weibull distribution. What is the probability that there are more than 15 positions unfilled at any point in time? How many jobs within the department are filled on average? How many positions should the firm have in order for the head count of working employees to be 100 on average?
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…
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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…

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