Problem 1 (25 points) Assume the ten values provided to you represent the monthly demand for a product your company manufactures. 1 2 3 4 5 6 7 8 9 10 59 91 144 99 95 120 63 100 95 95 a). (10 points) Fit an exponential smoothing model to this data. Using an MSE criterion, derive the value of alpha that best fits this data (your answer should be within 0.05 of the optimal value of alpha for this data set). Using this model, what is your predicted demand for the next period. (Hint - use the average of the ten observations as the seed for your models - this means only the last 9 values should be compared) b). (10 points) Fit a moving average model to this data. Consider windows of 2, 3 and 4 months and compare these models using the MAD criteria. Which model is the best? Based on the best model, what is your prediction for the next period? (Hint - since a 4-month moving average is not possible for months 1-4, your comparisons should be based in months 5-10.) c). (5 points) Compare the best models from parts a and b. Which model would you choose and what is your best estimate of the demand for period 11? (Hint - your comparison should be quantitative and well-justified.)