Favors Distribution Company purchases small imported trinkets in bulk, packages
ID: 459476 • Letter: F
Question
Favors Distribution Company purchases small imported trinkets in bulk, packages them, and sells them to retail stores. The managers are conducting an inventory control study of all their items. The following data are for one such item, which is not seasonal.
a. Use a trend projection to estimate the relationship between time and sales (state the equation). b. Calculate forecasts for the first four months of the next year. 1 2 3 4 5 6 7 8 9 10 11 12 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Sales 51 55 54 57 50 68 66 59 67 69 75 73
Explanation / Answer
Month Month(X) Sales(Y) X^2 Y^2 XY a b c = a^2 d = b^2 e = a*b Jan 1 51 1 2601 51 Feb 2 55 4 3025 110 Mar 3 54 9 2916 162 Apr 4 57 16 3249 228 May 5 50 25 2500 250 Jun 6 68 36 4624 408 Jul 7 66 49 4356 462 Aug 8 59 64 3481 472 Sep 9 67 81 4489 603 Oct 10 69 100 4761 690 Nov 11 75 121 5625 825 Dec 12 73 144 5329 876 78 744 650 46956 5137 Linear Trend Equation is given as= a + Bx a = [(y - bx) / n b = [nxy - (x * y)] / [(n * x^2) - (x)^2)] n = 12 b = (12 * 5137 - 78 * 744) / (12 * 650 - 78^2) = 3612 / 1716 = 2.1049 a = (744 - 2.1049 * 78) / 12 = 48.3182 Equation is given as 48.3182 + 2.1049x Forecast for First four months for next year Month Month(X) Alpha (a) bx Forecast x y z = x * 2.1049 y+z Jan 13 48.3182 27.3636 75.6818 Feb 14 48.3182 29.4685 77.7867 Mar 15 48.3182 31.5734 79.8916 Apr 16 48.3182 33.6783 81.9965
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