Question

A can-opener manufacturer has had monthly sales for a seven-month period as follows: Month Sales February 16 March 18 April 21 May 20 June 18 July 22 August 24

a. Plot the data to determine their pattern.
b. Forecast September’s sales volume using each of the following: - a three-month moving average - a weighted moving average using the following weights: 0.5 for August. 0.2 for July, and 0.3 for June. - Exponential smoothing with alpha = 0.2

Answer 1

To forecast September's sales for a can-opener manufacturer, three methods were used: the three-month moving average, resulting in approximately 21 units; weighted moving average with specific weights for the last three months, resulting in approximately 21 units; and exponential smoothing with α = 0.2, resulting in a forecast of 24 units.

Step-by-step explanation:

Forecasting September Sales Volume

To determine the sales pattern, plotting the given data, we see a general increasing trend in the monthly sales from February (16) to August (24). Now, let's forecast September's sales volume using different methods.

Three-Month Moving Average

To calculate the three-month moving average for September, we average the sales from June, July, and August: (18 + 22 + 24) / 3 = 64 / 3 = 21.33. Thus, we'd predict September's sales to be approximately 21 units.

Weighted Moving Average

Using the provided weights for the weighted moving average, the calculation is as follows: (18 × 0.3) + (22 × 0.2) + (24 × 0.5) = 21.4. Hence, the forecast for September is about 21 units, considering the weights for each month.

Exponential Smoothing

Using exponential smoothing with α (alpha) = 0.2 and assuming that the forecast for August was the actual August sales (24), the formula used will be: Forecast for September = α × Actual in August + (1 - α) × Forecast for August. Substituting the values, we get: 0.2 × 24 + 0.8 × 24 = 24. The forecast for September remains the same as August, 24 units.