Use mathematical induction to show that when n is an exact power of 2, the solution of the recurrence t(n) =¨2 if n = 2 2t(n/2)+ n if n = 2k, for k > 1 is t(n) = n lg(n).

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.