Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour x is given by x(t) = -4t^2+20t+92, where t is the number of hours since 10 AM, 0<=t<=4. a. If the price were raised to $3 per hot dog with no change in the x(t) equation, which hour would produce the most revenue? Why?
b. If the price were dropped to $1 per hot dog, but that price drop caused the number of sales to increase according to the function x(t) = -9t^2+22t+138, would the vendor make more money at the original $2 price, or at the $1 price?