An oil company acquires a drilling machine. The drilling machine will depreciate at the rate g(t) million dollars per year and will accumulate maintenance costs at the rate m(t) million dollars per year. Therefore, the cost function for this machine is c(t) = 1 t t 0 g(s) m(s) ds. (a) Show that the critical points of c(t) occur at t where c(t) = g(t) m(t). (b) Suppose that g(t) = {1 3 1 90 t if 0 < t 30, 0 if t > 30 and m(t) = t2 2580 for t 0. Find a formula for D(t) the total depreciation after t years. Hint: D(t) = g(t). (c) Determine the length of time T for the total depreciation to equal 5 million dollars. (d) Determine the absolute minimum of c(t) on (0, T