6. [Dynamic Programming, 20 points] Suppose you're consulting for a company that manufactures PC equipment and ships it to distributors all over the country. For each of the next n weeks, they have a projected supply si of equipment (measured in pounds), which has to be shipped by an air freight carrier. Each week's supply can be carried by one of two air freight companies, A or B Company A charges a fixed rate r per pound (so it costs r s to ship a week's supply s:). Company B makes contracts for a fixed amount c per week, independent of the weight. However, contracts with company B must be made in blocks of four consecutive weeks at a time. A schedule, for the PC company, is a choice of air freight company (A or B) for each of the n weeks, with the restriction that company B, whenever it is chosen, must be chosen for blocks of four contiguous weeks at a time. The cost of a schedule is the total amount pair to company A and B, according to the description above. Give a polynomial-time algorithm that takes a sequence of supply values s1,82 and returns a schedule of minimum cost. For example, if r = 1, c = 10 and the sequence of values is 11, 9, 9, 12, 12, 12, 12, 9, 9, 11, then the optimal schedule would be A,A,A,B,B,B,B,A,A,A Hint: Let OPT(i) denote the minimum cost of a solution for weeks 1 throughi