Determine the moth of maximum and minimun sales?

Question

Use a graphing utility to graph the sales function over 1 year,where s is the sales in thousands of units and t is the moth, with t=1 corresponds to january.Determine the moth of maximun and minimum sales.S=84.50 + 53.75 sin(pi)t/6

Answer 1

t =1    to    t=12

 

sin x has a max value of 1 and a min value of -1

 

1*53.75 would add the most to 84.50.

 

-1(53.75) would produce the lowest because it subtracts the highest possible value for that term from 84.50.

 

 

t(pi/6) for 1 to 12 = pi/6   to 2pi

 

On that interval,  sin x would hit it's max at sin pi/2 (90 degrees)

 

pi/2 = t(pi)/6

 

6pi = 2t(pi)

 

t = 3

 

So for t=3, 84.50 + 53.75 sin ((3pi)/6) will have it's greatest value.  

The month for the highest sales is March.

    84.50

+  53.75

---------

$ 138.25

 

 

 

The only place that sin (t)(pi)/6 = -1 is where:

 

t(pi)/6 = 3pi/2    (270 degrees)

 

18pi = 2t(pi)

 

2t = 18, so t = 9.  The month for the lowest sales would be September.

 

 84.50
-53.75
---------
$30.75

 

Answer 2

Its a sign curve with max at pi/2 (sin pi/2 = 1) and minumum ay 3pi/2 ( sin 3pi/2 = -1)

 

at t= 0; S = 84.5

 

For max S, Sin(pi t/6) = 1

 sin(pi t/6) = sin pi/2

 

pi t/6 = pi/2

t = 3 i.e month of March

 

For min S, Sin(pi t/6) = -1

sin (pi t/6) = sin (3pi/2)

pi t/6 = 3 pi/2

t= 9 i.e. month of September

 

:)