MGMT 5312 Fall 2023- Final Exam

This is an open book exam but you are NOT allowed to consult with anyone. Violation of code of Academic Integrity will lead to severe penalty.

You have 2 hrs. and 30 minutes to complete and upload the exam

Q1. (33 points)

Southern Oil company produces two grades of gasolene: regular and premium.

The profit contributions are $ 0.3 per gallon for regular gasolene & $ 0.50 per gallon for premium gasolene.

Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasolene contans 0.6 gallons of grade A crude oil.

For the next production period, Southern has 18,000 gallons of grade A crude oil available.

The refiner used to produce the gasolenes has a production capacity of 50,000 gallons for the next production period.

Southern Oil’s distributors have indicated that the demand for premium gasoline for the next production period will be at most 20,000 gallons.

Set up the problem as an LP problem and determine the optimal solution using

Year Quarter Revenue Q2. (33 points)

1 1 20 The data shows the Sales Revenue for an organization for 5 years for each quarter.

2 100 a. Use mutiple regression model with dummy varaibles as below to develop an equation to account for seasonal effects in the data.

3 175 Qtr1 = 1 if Qtr1, 0 otherwise; Qtr2 = 1 if Qtr2, 0 otherwise; Qtr3 = 1 if Qtr3, 0 otherwise;

4 13 b. Based on (a), compute estimates for quarterly sales for year 6.

2 1 37 c. Let Period= 1 refer to observation in quarter 1 of year 1, Period= 2 refer to observation in quarter 2 of year 1, …Period= 20 refer to observation in quarter 4 of year 5.

2 136 Based on the dummy variables defined in (a) and the variable Period, develop an equation to account for any seaasonal effects and linear trend in the time series.

3 245 d. Based on the seasonal effects and the linear trend, compute estimates for quarterly sales for year 6.

4 26 e. Is the model in (a) or that in (c), more effective? Give reason.

3 1 75

2 155

3 326

4 48

4 1 92

2 202

3 384

4 82

5 1 176

2 282

3 445

4 181

Q3. (34 points)

Comet Dry Cleaners specializes in same-day dry cleaning. Presently, an average of 20 garments are held over for the next day because of capacity constraints.

The outlet manager is contemplating expanding to elimate the backlog.

A probability distribution of garments received and the maximum number of garments that can be cleaned after expansion is given below.

Run a simulation of 50 days to determine the daily backlog (garments received less garments cleaned)

Determine the average daily backlog, if any, after expansion.

If the cost associated with garments being held over is $ 25 per garment, and the added cost of expansion is $200 per day, is the saving enough to justify expansion?

Note: A suggested template is provided for use.

```
Probability "Beginning
```

Range of Prob.” “Garments Received

per day” Trial “Random

Number” “Garments received

per day” Trial “Random

Number” “Garments cleaned

per day” Backlog

0.1 50 1 1

0.25 60 2 2

0.3 70 3 3

0.25 80 4 4

0.1 90 5 5

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Probability “Beginning

Range of Prob.” “Garments Cleaned

per day” 10 10

0.3 50 11 11

0.4 60 12 12

0.3 70 13 13

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