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Q1. Rider is a midsize manufacturing company that produces high-end customizable motorcycles. Last year they rolled out 210 bikes (at a sales price of $53,500 each) using the following inputs (with their associated costs):
Inputs | Amount | Cost ($) |
---|---|---|
Labor Hours | 16,400 | $27.00 |
Sheet metal (square feet) | 1,650 | $3.21 |
Tires | 320 | $57.29 |
Paint (gallons) | 520 | $25.36 |
Energy (kWh) | 18,427,790 | $0.15 |
- What was last year’s single-factor productivity for Rider in terms of labor hours (not dollars)? (Display your answer to four decimal places.) 0.0128
- What was last year’s single-factor productivity for Rider in terms of sheet metal (square feet)? (Display your answer to four decimal places.) 0.1273
- What was last year’s single-factor productivity for Rider in terms of paint (gallons)? (Display your answer to four decimal places.) 0.4038
- What was last year’s multi-factor productivity for Rider in terms of dollars? (Display your answer to two decimal places. 3.46
Q2. A local fertilizer plant has a design capacity of 390 tons per week with an effective capacity of 330 tons per week. It regularly produces 300 per week.
What is the plant’s efficiency rate? 90.91%
- Write your answer as a percentage.
- Display your answer to two decimal places
What is the plant’s utilization rate? 76.92%
- Write your answer as a percentage.
- Display your answer to two decimal places.
Q3. iDetail ran a booming IBC business during the winter semester. They would detail automobiles while customers waited. With their initial way of cleaning vehicles–sequentially, like an assembly line–they were able to detail 3 vehicles per hour utilizing 8 workers. After some thought and experimentation, they changed the layout by placing multiple vehicles in adjacent stalls and working on them somewhat simultaneously. After these changes they were able to service 4 vehicles per hour with 7 workers.
- Prior to making the changes described above, what was the single-factor productivity for iDetail, in terms of workers? (Display your answer to two decimal places.) 0.38
- After making the changes described above, what was the single-factor productivity for iDetail, in terms of workers? (Display your answer to two decimal places.) 0.57
- After making the changes described above, by how much did the single-factor productivity improve for iDetail? (Write your answer as a percentage,and display your answer to two decimal places.) 52.38
Q4. Etched Impressions produces custom laser-etched artwork on a variety of flat wood surfaces. They recently purchased some new equipment which should help them be more productive. Data from the last two months’ production can be found in the following table:
Outputs / Inputs | Price/Cost per Unit ($) | Last Month | This Month |
---|---|---|---|
Units Produced | $22 | 870 | 1,000 |
Labor (hours) | $10.75 | 505 | 415 |
Wood (feet) | $2.59 | 980 | 880 |
Energy (BTUs) | $0.64 | 3,080 | 3,190 |
What was last month’s single-factor productivity for Etched Impressions in terms of labor dollars? In other words, for every dollar spent on labor, how many dollars of sales would they obtain? (Round your answer to two decimal places.) 3.53
From last month to this month, by what percentage did Etched Impressions’ productivity increase or decrease in terms of Energy (BTUs and units produced, not dollars)? 11.06%
- Write your answer as a percentage.
- Display your answer to two decimal places.
- Put a minus sign (“-“) in front of your answer if the answer is a negative number (i.e., a decrease).
What was this month’s multi-factor productivity for Etched Impressions in terms of dollars? (In other words, how many dollars of revenue did each dollar of inputs produce? (Round your answer to two decimal places.) 2.51
By what percentage did Etched Impression’s multi-factor productivity improve, in terms of dollars, from last month to this month? (Write your answer as a percentage, and display your answer to two decimal places.) 30.05%
Q5. Madison Memorial Hopsital is considering purchasing a new ambulance. The decision will rest partly on the anticipated mileage to be driven this year (2024). The miles driven during the past eight years are as follows:
Year | Miles Driven |
---|---|
2016 | 3,052 |
2017 | 1,002 |
2018 | 3,294 |
2019 | 3,108 |
2020 | 2,243 |
2021 | 2,010 |
2022 | 1,366 |
2023 | 1,453 |
Using a 4-year moving average, what would be the forecast for the miles to be driven in 2024? (Display your answer to the nearest whole number.) 1,768
Using a 4-year weighted moving average (with last year’s weight as 0.7, two years previous as 0.1; three years previous as 0.1, and four years previous as 0.1) what is the forecast for 2024? (Display your answer to the nearest whole number.) 1,579
Q6. if they should recommend hiring more state police based on the average number of highway miles logged by each driver in the state. The decision will rest partly on the anticipated highway miles to be driven next year by each driver. The miles driven during the past five years are as follows:
Year | Miles Driven |
---|---|
2019 | 87,694 |
2020 | 96,524 |
2021 | 91,281 |
2022 | 85,008 |
2023 | 93,241 |
What is the 2-year moving average forecast for miles to be driven in 2024? (Display your answer to the nearest whole number.) 89,125
What is the 3-year moving average forecast for miles to be driven in 2024? (Display your answer to the nearest whole number.) 89,843
What is the 4-year moving average forecast for miles to be driven in 2024? (Display your answer to the nearest whole number.) 91,514
Using a 4-year weighted moving average (with last year’s weight as 0.5, the year before that as 0.2, the year before that as 0.2, and the year before that as 0.1) what is the forecast for 2024? (Display your answer to the nearest whole number.) 91,531
Q7. Mitchell’s Mills is a startup looking to break into the preparedness market with a revolutionary new wheat grinder called the WG1. Since Mitchell’s is a new company they do not have any historical data for sales of its flagship product, but they estimate they will be able to sell 412 in the month of April. The table below contains actual sales data for April and each of the succeeding five months (through September):
Month | WG1s Sold | Forecast |
---|---|---|
Apr | 392 | 412 |
May | 424 | |
Jun | 475 | |
Jul | 468 | |
Aug | 447 | |
Sep | 419 |
Suppose it was the beginning of May and you were asked to develop a forecast for the month of May. Your only actual sales data was for the month of April. Because of this paucity of data you decide to use the exponential smoothing method for the construction of your forecasting model. You determine that an alpha value of 0.65 would be appropriate.
Based on the above information, what would have been your forecast for the month of May? (Display your answer to two decimal places.) 399.00
If you follow this same forecasting process through all the months, continuing with June and going through September, what would be the forecast in the month of September? (Display your answer to two decimal places.) 452.65
What is the MAD for this forecast (based on six months of forecasts—April through September)? (Display your answer to two decimal places.) 28.07
What is the MAPE for this forecast (based on six months of forecasts—April through September)? (Write your answer as a percentage, and display your answer to two decimal places.) 6.37%
Q8. Enrollment numbers at BYU-Idaho over the last four years are as follows:
Semester | 2020 | 2021 | 2022 | 2023 |
---|---|---|---|---|
Winter | 15,270 | 14,094 | 15,350 | 14,673 |
Spring | 14,179 | 13,743 | 13,962 | 13,186 |
Fall | 15,595 | 17,931 | 15,620 | 15,962 |
What is the seasonal index for the winter semester? (Display your answer to two decimal places.) 0.99
What is the seasonal index for the spring semester? (Display your answer to two decimal places.) 0.92
What is the seasonal index for the fall semester? (Display your answer to two decimal places.) 1.09
Suppose for the 2024 school year BYU-Idaho is expecting a total of 48,000 students. Based on this projection, how many students should they expect to enroll in the fall semester? (Display your answer to the nearest whole number.) 52,320
Q9. Universal Studios is in the process of opening a new theme park in California and wants to forecast the number of visitors it should expect each season. They have decided to use data from its Florida theme park as a basis for forecasting attendance at the new California park. The table below shows the total attendance numbers, by season, for the Florida theme park during the years 2020 through 2023:
Season | 2020 | 2021 | 2022 | 2023 |
---|---|---|---|---|
Winter | 842,000 | 868,000 | 895,000 | 799,000 |
Spring | 1,425,000 | 1,378,000 | 1,407,000 | 1,304,000 |
Summer | 1,426,000 | 1,420,000 | 1,536,000 | 1,499,000 |
Fall | 769,000 | 833,000 | 702,000 | 769,000 |
What is the seasonal index for spring? (Display your answer to two decimal places.) 1.23
What is the seasonal index for summer? (Display your answer to two decimal places.) 1.32
What is the seasonal index for fall? (Display your answer to two decimal places.) 0.69
Suppose the 2024 forecast calls for a total of 4,600,000 visitors. How many visitors should they expect in the winter? (Display your answer to the nearest whole number.) 3,496,000
Q10. The Cocoa Bean sells hot chocolate during the year. This is shown in the following table:
Month | Avg Temp | Sales |
---|---|---|
Jan | 20 | 229 |
Feb | 18 | 203 |
Mar | 44 | 249 |
Apr | 54 | 151 |
May | 73 | 87 |
Jun | 83 | 87 |
Jul | 73 | 47 |
Aug | 90 | 56 |
Sep | 88 | 100 |
Oct | 64 | 131 |
Nov | 38 | 139 |
What would the December sales forecast be if the average temperature that month was projected to be 21? (Display your answer to two decimal places.) 218.15
What is the r-value (correlation coefficient) for this set of data? (Display your answer to two decimal places. If you get a negative number then put a minus sign before your number.) -0.84
The correlation coefficient (from the previous question) indicates that as temperature goes DOWN, sales tend to go: UP
The Cocoa Bean has determined that the magnitude of a correlation coefficient (whether positive or negative) is considered strong if it is 0.70 or more, moderate if it is between 0.40 and 0.69, and weak/none if it is below 0.40. Based on your analysis, the correlation between temperature and hot chocolate sales is: STRONG