9. We studied one way to solve the transportation problem, namely to represent it as an LP instance and use the simplex method Consider a different algorithm, based on the greedy approach: given an instance of the transportation problem, represented as a chart like this (just an example, with 3 factories and 5 stores) 1 2 34 5 we find the cell with the smallest cost_ in this example, row 3 and column 2 - and write the biggest value we can in that cell in this case, 6 and note that the amounts available for that row and col- umn have been reduced, obtaining this chart 10 15 12 8 6 107 6 10 15 We repeat this process, fill- ing in cells in a greedy fash- ion, until all the materials have been shipped 6 6 8 10 7 6 0 a. [4 points] Show your understanding of this greedy algorithm by finishing the process for this example- write your changes directly in the cells and next to the row and column totals on the chart given above. Break ties -when two cells have the same cost-any way you like b. [4 points] Prove that this greedy algorithm does not always find the optimal result by finding an example sportation problem chart, show how the for which it does not work. To do this, you must draw a trar greedy approach works on it, and show a different choice that produces a better objective function value. Note that the objective function value is the sum over all the cells of the product of the cost number and the amount shipped for the cell Hint: consider a chart with just 2 factories and 2 stores, with each factory producing 1 item, and each store wanting 1 item