You are consulting for a trucking company that does a large amount ofbusiness shipping packages between new york and boston. the volume ishigh enough that they have to send a number of trucks each day betweenthe two locations. trucks have a fixed limit w on the maximum amountof weight they are allowed to carry. boxes arrive at the new york stationone by one, and each package i has a weight wi. the trucking stationis quite small, so at most one truck can be at the station at any time. company policy requires that boxes are shipped in the order they arrive; otherwise, a customer might get upset upon seeing a box that arrivedafter his make it to boston faster. at the moment, the company is usinga simple greedy algorithm for packing: they pack boxes in the order theyarrive, and whenever the next box does not fit, they send the truck on itsway. but they wonder if they might be using too many trucks, and theywant your opinion on whether the situation can be improved. here ishow they are thinking. maybe one could decrease the number of trucksneeded by sometimes sending off a truck that was less full, and in thisway allow the next few trucks to be better packed. prove that, for a given set of boxes with specified weights, the greedyalgorithm currently in use actually minimizes the number of trucks thatare needed. your proof should follow the type of analysis we used forthe interval scheduling problem: it should establish the optimality of thisgreedy packing algorithm by identifying a measure under which it