3. ABC a manufacturer of large size pressure cookers, produces and sells three models of cookers. While market demands pose no restriction, the capacity to produce is currently constrained by the limited supplies of special grade aluminium limited to 1500kg per week and machine processing time limited to 1200 hours per week. In order to determine the optimal product mix to maximize weekly contribution, a linear programming model was formulated as below. ET Online College 2 Maximize Z= 60X1+ 40X2+ 80X3 Subject to 6X1+ 3X2+ 5X3 1500 (Aluminium) 3X1+ 4X2+ 5X3 1200 (Machine Hours) X1, X2, X3 0 Using the simplex method, the following tableau was obtained BASIC V CJ 60 40 80 0 0 X1 X2 X3 S1 S2 RHS X1 _ 1 -1/3 0 1/3 -1/3 0 1 1 -1/5 2/5 100 X3 _ 180 ZI CJ-ZI _ _ _ _ _ _ _ _ _ _ _ _ Required: a) Fill in all the numerical values in the above table b) Is the current solution optimal? If not, carry out the iterations until an optimal solution is reached c) Analyze the sensitivity of the optimal solution to the following changes d) Due to a machine breakdown, the machine hours available gets reduced to 1050 hours e) An additional quantity of 150 kg of aluminum can be obtained f) Formulate the dual of the problem and determine the dual solution from the primal optimal tableau