Suppose that a company decides to raise capital by selling stock. Over the next 10 years the average monthly price of the stock fluctuates according to the rule S(t) = 0.08t1.5 1.08t + 53.75 where S(t) is in dollars per share and t is the number of months since the stock was first offered for sale (this means that S(t) is only valid on the interval [0, 120]). Determine the maximum and minimum prices of the stock (in dollars and cents) and when these prices occurred