Answered: Amex PLC has gathered following…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Amex PLC has gathered following information on the sales of face mask from April 2020 to September 2020.

You are required to;
a. Using linear trend equation forecast the sales of face masks for October 2020.

b. Calculate the forecasted sales difference if you use 3-period weighted moving average designed with the following weights: July 0.2, August 0.3 and September 0.5.

Month
Sales ($)
April
17,000
May
18,000
June
19,500
July
22,000
August
21,000
September
23,000

Expert Solution

Step 1

Given, information gathered by PLC on the sales of face mask from April 2020 to September 2020.

a) The linear trend equation for forecasting the sales of face masks for October 2020 is given as-

$μ_{t} = a + b t$

Where,

$a = \frac{\sum_{t} μ_{t}}{n}$

$b = \frac{\sum_{t} t \times μ_{t}}{\sum_{t} t^{2}}$

Let us assume the months from April to October be 1,2,3,....,7

Let,

$\begin{array}{rcl} t & = & m o n t h - \frac{7}{2} \\ = & m o n t h - 3.5 [s u c h t h a t \sum_{t} t = 0] \end{array}$

The table below shows the required calculation-

Month	t=month-3.5	Sales ( $μ_{t}$ )	t²	$t \times μ_{t}$
April (1)	-2.5	17000	6.25	-42500
May (2)	-1.5	18000	2.25	-27000
June (3)	-0.5	19500	0.25	-9750
July (4)	0.5	22000	0.25	11000
August (5)	1.5	21000	2.25	31500
September (6)	2.5	23000	6.25	57500
Total	0	120500	17.5	20750

Therefore,

$\begin{array}{rcl} a & = & \frac{120500}{6} \\ = & 20083.33 \end{array}$

$\begin{array}{rcl} b & = & \frac{20750}{17.5} \\ = & 1185.71 \end{array}$

Therefore, the linear trend equation for forecasting the sales of face masks for October 2020 is obtained as-

$μ_{t} = 20083.33 + (1185.71) t$

The forecasted value of sales for October (7) is obtained as-

$\begin{array}{rcl} μ_{t} & = & 20083.33 + (1185.71) \times (7 - 3.5) \\ = & 20083.33 + 4149.985 \\ = & 24233.315 \end{array}$

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