The monthly sales (in thousands of units) of a seasonal product are approximated by
S= 74.50 + 43.75 sin pi t/6
Where t is time in months, with t=1 corresponding to January. Determine the months when sales exceed 100,000 units

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25-11-2016
Mathematics

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The monthly sales (in thousands of units) of a seasonal product are approximated by
S= 74.50 + 43.75 sin pi t/6
Where t is time in months, with t=1 corresponding to January. Determine the months when sales exceed 100,000 units

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Аноним Аноним · Answer 1 · 2016-11-28T03:16:00+01:00

Don't forget S is measured in thousands of units so you are solving for :

100 < 74.5 + 43.75Sin(πt/6)
25.5 < 43.75Sin(πt/6)
Sin(πt/6) >25.5/43.75 = 0.582857
ASrcSin(πt/6) > 0.62224 radians
πt/6 > 0.62224
t > 6 x 0.62224/π = 1.1884 (4dp)

This initial value occurs when the sine value is increasing and it will reach its maximum value of 1 when Sin(πt/6) = Sinπ/2, that is when t = 3.
Consequently, monthly sales exceed 100,000 during the period between t = 1.1884 and 4.8116
[3 - 1.1884 = 1.8116 so the other extreme occurs at 3 + 1.8116]

Note : on the basis of these calculations, January is 0 ≤ t < 1 : February is 1 ≤ t < 2 :....May is 4 ≤ t < 5
So the period when sales exceed 100,000 occurs between Feb 6 and May 25 and annually thereafter.

The monthly sales (in thousands of units) of a seasonal product are approximated by S= 74.50 + 43.75 sin pi t/6 Where t is time in months, with t=1 corresponding to January. Determine the months when sales exceed 100,000 units

Respuesta :

Otras preguntas

The monthly sales (in thousands of units) of a seasonal product are approximated by
S= 74.50 + 43.75 sin pi t/6
Where t is time in months, with t=1 corresponding to January. Determine the months when sales exceed 100,000 units