A company that produces snowboards, which are seasonal projects, forecasts monthly sales for one year to be...

Question

S = 77.00 + 45.50 cos (πt /6)

where S is the sales in thousands of units and t is the time in months, with t = 1 corresponding to January.

(a) Use a graphing utility to graph the sales function over the one-year period.

left graph = a

right graph = b

below to the left = c

below to the right = d

(b) Use the graph in part (a) to determine the months of maximum and minimum sales

minimum:

maximum:

Answer 1

S =77 +45.50 Cos ( pit/6)

at t=0

S = 77+ 45.50 = 122.50

So graph c is correct

For Max or Min dS/dt = 0

dS/dt = - 45.50 (pi/6) Sin pit/6 ) =0

So for max t = 0, 12, 24 ,... years

For Min t = 6, 18,......... years