Question

Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by x(t) = −4t2 + 20t + 52,where t is the number of hours since 10 AM, 0 ≤ t ≤ 4. (a) Find an expression for the revenue per hour R as a function of x.
R(x) =
(b) Find and simplify (R x)(t).
(c) What is the revenue per hour at noon?