The revenue of McMenamy's fish shanty is approximately
R(t)=2(5-4cos (pi/6)t) (0<t<12)
during the t week (t=1 corresponds to the first week of June) where R is measured in thousands of dollars. On what week is the marginal revenue zero?
Marginal R is dR/dt = R'(t)
R(t) = 2{5 -4cos[(pi/6)t]}
R'(t) = 2[(-4)(-sin[pi/6)t] *(pi/6)]
R'(t) = (8pi/6)sin[(pi/6)t]
When R'(t) = 0.
0 = (8pi/6)sin[(pi/6)t]
0 = sin[(pi/6)t]
(pi/6)t = arcsin(0)
(pi/6)t = 0, or 2pi
When (pi/6)t = 0,
t = 0 -----------------**
When (pi/6)t = 2pi,
t = (2pi)/(pi/6) = 12 ----**
Therefore, the marginal revenue is zero at week zero and week 12. ----answer.