3. (20 points) In a 34 transportation problem, let x be the amount shipped from source i to destination j and let c; be the corresponding cost per unit transported. The amounts of supply at sources 1,2 , and 3 are 15,25 , and 10 units, respectively. The demands at destinations 1,2,3 and 4 are 5,15,15 and 15 units, respectively. Assume that the starting northwest-comer solution is optimal and that the associated values of the multiplicrs in MODI are: u1=0,u2=5,u3=3,v1=10,v2=2,v3=4,v4=15 a. Find the associated cost ( 11 points). b. Determine the smallest value of c for each noi.vasic variablo that will maintain the optimality of the northwest-corner solution ( 9 points)