Create a Line Chart to illustrate the data Period (t) De ✓ Solved

Create a Line Chart to illustrate the data Period (t) Demand.

Moving Average:

  • Compute the Forecast for the next period using a 3-period moving average.

  • Calculate the following Forecast Error measures for this method:

    • Mean Absolute Deviation (MAD)

    • Mean Square Error (MSE)

    • Mean Absolute Percentage Error (MAPE)

  • Create a Line chart to illustrate the demand and forecast values.

Exponential Smoothing Method:

  • Compute the Forecast for the next period using simple exponential smoothing with 0.3 as the smoothing constant.

  • Calculate the following Forecast Error measures for this method:

    • Mean Absolute Deviation (MAD)

    • Mean Square Error (MSE)

    • Mean Absolute Percentage Error (MAPE)

  • Create a Line chart to illustrate the demand and forecast values.

Linear Trend:

  • Compute the Forecast for the next period using a simple linear regression.

  • Calculate the following Forecast Error measures for this method:

    • Mean Absolute Deviation (MAD)

    • Mean Square Error (MSE)

    • Mean Absolute Percentage Error (MAPE)

  • Create a Line chart to illustrate the demand and forecast values.

Method Selection:

  • Determine which of the forecasting methods is more accurate based on the Mean Absolute Percentage Error (MAPE).

A garage band wants to hold a concert. The expected crowd is 2,600. The average expenditure on concessions is $39. Tickets sell for $27 each, and the band's profit is 74% of the gate and concession sales minus a fixed cost of $22,000. Develop a mathematical model and implement it on a spreadsheet to find the band's expected profit.

An electronics manufacturer launching a new device to the market. Fixed costs for production of the new device is $41,591. Analysis of the cost of materials and labor required resulting in estimated variable costs totaling $8.51 per device. A recent market research report showed that the device would sell reasonably well at a price of $37 per unit.

  • Build a spreadsheet model to calculate the profit or loss for a given demand.

  • Use Goal Seek to determine the number of units that the manufacturer must sell to break even (profit=0).

  • Use Goal Seek to determine the price per unit of the device to break even with an estimated demand of 5,250 units.

  • Create a one way data table to vary demand from 1000 to 6000 in increments of 1000 to assess the sensitivity of profit to demand.

  • Use a TWO WAY data table to vary demand from 1000 to 6000 in increments of 1000 and vary price from 40 to 60 in increments of $5.

Paper For Above Instructions

This paper addresses numerous forecasting methods and financial modeling approaches that can enhance decision-making for businesses, particularly in predictive analytics and financial planning.

1. Time Series Forecasting

Forecasting the demand over time is a pivotal aspect of operations management. A line chart visualizing historical data helps in understanding trends. For the provided data period (t), one can initially create a line chart depicting demand over time. This will serve as the foundational visual representation from which we can derive more intricate analytical insights.

2. Moving Averages

Applying a 3-period moving average is a common practice in forecasting. In this method, the forecast for the next period is calculated by averaging the demand of the previous three periods. If, for instance, the demand in periods t-1 to t-3 was 100, 150, and 200 units respectively, the forecast for period t would be (100 + 150 + 200) / 3 = 150 units. Forecast error metrics, such as the Mean Absolute Deviation (MAD), Mean Square Error (MSE), and Mean Absolute Percentage Error (MAPE), are computed to evaluate the method's accuracy.

3. Exponential Smoothing

Simple exponential smoothing is another effective method, particularly when historical data trends lean towards stability without seasonality. The smoothing constant, in this case 0.3, weighs recent observations more heavily than older ones. For example, if the previous period's forecast was 150 and the actual demand was 180, the new forecast can be updated as: Forecast_next = (Smoothing Constant Actual_demand) + ((1 - Smoothing Constant) Previous_forecast). Using this formula, we can derive the demand forecast, and again compute MAD, MSE, and MAPE to assess performance.

4. Linear Regression

Applying linear regression to forecast the next period's demand hinges on establishing a relationship between time and demand. The linear model, expressed as Demand = m*t + b, where m is the slope and b is the intercept, can provide a linear trend line. Once the slope and intercept are calculated, we can predict future demand and again compute relevant error metrics to compare with previous methods.

5. Selection of the Best Method

To determine the best forecasting method among those applied, one must analyze the computed MAPE values. The forecasting method yielding the lowest MAPE indicates the highest accuracy and should be selected for further utilization. Analyzing these metrics in conjunction with visual data representations exudes clarity in decision-making.

6. Financial Modeling for Concert Profitability

In the scope of the garage band's profitability, we outline a mathematical model where expected income from tickets and concessions directly affects profit. The expected income from 2,600 attendees purchasing tickets at $27 each results in revenue. With a fixed cost of $22,000, the total income minus costs will reveal the expected profitability. The concession expenditure must also be factored to gauge total income accurately:

  • Total Ticket Revenue = 2,600 * 27

  • Total Concession Revenue = 2,600 * 39

  • Profit = (Total Ticket Revenue + Total Concession Revenue) - Fixed Costs

7. Manufacturing Break-even Analysis

For the electronics manufacturer, calculating break-even points necessitates analysis of fixed costs, variable costs, and pricing strategies. Establishing a spreadsheet model to simulate profit or loss at variable demand levels provides pivotal insights. Utilizing Goal Seek functionality in spreadsheet programs allows one to efficiently derive break-even units necessary at a sales price of $37 per device.

8. Sensitivity Analysis Using Data Tables

The final component involves creating one-way and two-way data tables to analyze how changes in demand and price affect profitability. Altering demand from 1,000 to 6,000 units and adjusting prices between $40 and $60 provides clarity on profit sensitivity. For instance, if at a price point of $50 and a demand of 3,000 units leads to a specific loss or profit, it becomes crucial to highlight that result within the data table for comprehensive analysis.

Conclusion

In conclusion, carefully implementing various forecasting techniques alongside rigorous financial modeling not only aids in accurate demand prediction but also enhances overall profitability assessments for operational decisions.

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