Let St21555cos6t be the sales function over 1 year where S i

Let S(t)=21.55.5cos(/6t) be the sales function over 1 year where S is sales in thousands of dollars and t is time in months, with t=1 corresponding to January. Which month has minimum sales? What is the minimum number of sales?

a)December; $16,000

b) December; $27,000

c) June; $16,000

d) September; $16,000

e) June; $27,000

Solution

S(t)=21.55.5cos(/6t)

For min sales,
S\'= 0

Find S\'by deriving :
S\'= 0 - 5.5 * -sin(pit/6) * (pi/6)

S\'= 5.5pi/6 * sin(pi*t/6)

sin(pi*t/6) = 0

t = 0 or t = 12

Clearly, t = 0 does not make any sense

t = 12 means DEcember

When t = 12, we get :
S = 21.55.5cos(/6 * 12)
S = 21.5 - 5.5cos(2pi)
S = 21.5 - 5.5
S = 16

So, answer is :
December 16000 dollars

Option A