4. [12 marks] Suppose that S(t) = 30+60 cos / 21 (t 15) represents a company's profit (in thousands of dollars) from sales during week t [1, 52].

(a) Without the use of a calculator, determine the company's profit during week 36 . Interpret your result.

(b) Determine the maximum profit earned by the company in a week. During which week does the company earn its maximum profit?

(c) Define S(t) as a function in Maple (S(t) :=???) and plot S(t) in Maple for t [0, 52]. Over the 52 -week period, how many times does the company "break even" (have no profit or loss) after week 1?

(d) Algebraically determine the week(s) in which the company breaks even