With explanation pls!

13.MaX z = 5X1 + 4X2 +10X3 + 8X4 s.t. 1X1 + 1X2 + 1X3 + 1X4 3 120 (labor) 1X1 + 2X2 + 4X3 + 4X4 5 420 (material A) 2X1 + 4X2 + 2X3 + 4X4 3 380 (material B) 4X1 + 5X2 + 5X3 + 2X4 3 400 (material C) X1, X2, X3, X4 2 0 0 Price Sol'n Qty 5 4 10 8 0 Row Vector Vector Vector X1 X2 X3 X4 51 I 5 X1 20 1 6/9 0 0 12/9 II 8 X4 60 0 -2/9 0 1 11/9 III 0 S3 20 0 22/9 0 0 -40/9 IV 10 X3 40 0 5/9 1 0 -14/9 NC -Z -980 0 -28/9 0 0 -8/9 In each problem, do the following: a Write the dual problem State the value of each dual variable. b. c. State the value of the dual objective function. d. 0 52 -3/9 1/9 -2/ 9 2/9 -13/ 9 6/9 3/9 -6/ 9 Verify that total contribution is the sum of the contributions of the individual FESOU I'CES. e. Determine how much the price of X2 would have to increase before this process became protable. f. Would we utilize a proposed new process that has a prot contribution of $2 and consumes 1 unit of each productive resource? Would we utilize the process if it has a prot contribution of .95 and used 1 unit of the rst and third resources only