Maximum Revenue

Question

The total annual revenue (in billions of dollars) for the Boeing Corporation from 1990 to 2002 is given by
R(t)=-0.1(t-1)2+80
where t=0 is January 1, 1990. The annual revenue (also in billions of dollars) that Boeing made just from sales of its 737 airplane in the same period is given by A(t)=0.2(t-8)2+30


a)In what year and month was annual revenue excluding sales of 737s at a maximum?

b)What was that maximum revenue (in billion dollars per year)?

Answer 1

R(t) = 0.1(t-1)^2 + 80

where t = years since 1990, R= Total Revenue in thousands of dollars

Annual Revenue = A(t) = .2(t-8)^2 + 30

in what year and month is Revenue at a maximum??

what was the max revenue per year??

find R' =0, solve for t

.2(t-1) = 0

t = 1

plug back into original equation for R(t)

R(1) = 80= max Total Revenue

= $80,000