Answer:
The sale forecast for May is [tex]i= 120.56[/tex]
Step-by-step explanation:
From the question we are told that
The value of [tex]\alpha = 0.5[/tex]
Month January February March April
Observed sales a= 113 b= 122 c= 130 d= 116
The sales forecast for January is [tex]e = 115[/tex]
Generally the sales forecast for February is mathematically represented as
[tex]f = \alpha * a + [1- \alpha * ( e)][/tex]
=> [tex]f = 0.5 * 113 + [(1- 0.5) * (115)][/tex]
=> [tex]f =114[/tex]
Generally the sales forecast for March is mathematically represented as
[tex]g = \alpha * b + [(1- \alpha) * ( f)][/tex]
=> [tex]g = 0.5 * 122 + [(1- 0.5) * ( 118.5)][/tex]
=> [tex]g = 120.25[/tex]
Generally the sales forecast for April is mathematically represented as
[tex]h= \alpha * c + [(1- \alpha) * ( g )][/tex]
=> [tex]h= 0.5 * 130 + [(1- 0.5) * ( 120.25 )][/tex]
=> [tex]h= 125.125[/tex]
Generally the sales forecast for April is mathematically represented as
[tex]i= \alpha * d + [(1- \alpha) * ( h )][/tex]
=> [tex]i= 0.5 * 116 + [(1- 0.5) * ( 125.125 )][/tex]
=> [tex]i= 120.56[/tex]
