1. Dynamic Programming-Truck Allocation Problem (12 points). A manager of a nationwide A trucking company has 6 newly acquired trucks which he wishes to assign to three large cities A, B, and C. From past experience with similar situations he has determined the incremental profitability of increasing his fleet size in each of the three cities to be as shown in Table 1. There is an upper bound on the number of trucks allowable at any one citythe upper bound is 2 for city A and 3 for cities B and C. Find the optimal allocation of the new trucks to the three cities using dynamic programming. Table 1 Net profit from additional truck allocations.(in thousands of dollars) Trucks City A City B City C Allocated 0 0 23 50 0 20 45 60 2 30 38 59 3