A manufacturer has 4 products each requiring polishing and packing operations. For each product the time required for these operations is shown below (in minutes) as is the profit per unit sold. Considering the current labour force of the plant, the company estimates that each year they have 45,000 minutes of polishing time and 72,000 minutes of packing time available. Also, production requirements state that the total amount produced by product 1 and 4 should be exactly 12000 units and at least 5000 units of the second product should be produced. Assume that you can produce fractional amount of products. To find the optimal production amounts from each product to maximize the profit while obeying the time limitations the following LP is constructed: maxs.t.2.5x1+3.5x2+x3+4x45x1+3x2+2x3+2x445,0003x1+2x2+4x3+3x472,000x1+x4=12,000x25,000x1,x2,x3,x40 the optimal simplex tableau after applying big-M method and the Excel solver's sensitivity report: You are given that the inverse of the basis matrix corresponding to the above tableau is: B1=1/32/301/301002/35/312/31000 Ohiective Coll (Max) Decision Variable Cells Answer the following questions by using the information provided above. a-) Find the values of the 9 unknowns A, B, C, D, E, F, G, H and I. Explain how you attain each. b-) If you had the choice of increasing the RHS value of a single constraint by 1 unit, which constraint would you choose and why? c-)How many units should c1 increase such that there would be an alternate optimal solution with x1 in the basis? How would you determine this value from the Excel output? d-) What would happen when the RHS of constraint 3 is increased by 6,000 units? If the optimality gets disturbed, which type of feasibility would be lost and which simplex method would you use to fix this infeasibility? e-) What is the optimal solution for the part d. f-) What is the optimal value and the optimal solution when the objective coefficient of x2 is decreased by 2 units? If there are alternative optimal solutions, can you list them all? g-)Find the set of RHS vectors such that the current basis remains optimal