Question 6_(16 marks) The following table shows the sensitivity analysis for a LP problem. Adjustable Cells Final Reduced Objective Cell Name Value Cost Coefficient $B$10 No. of Units Product 1 50 0 25 $C$10 No. of Units Product 2 237.5 18 $D$10 No. of Units Product 3 0 -4.375 32 $E$10 No. of Units Product 4 268.75 0 15 Allowable Increase 13.625 4.5 4.375 6.6 Allowable Decrease 1E+30 5.5 1E+30 2.058823529 0 Constraints Cell Name $B$16 Department 1 time LHS $B$17 Department 2 time LHS $B$18 Material LHS $B$19 Min production level LHS Final Value 150 102.8125 1800 50 Shadow Price 41.25 0 2.25 - 13.625 Constraint R.H. Side 150 120 1800 50 Allowable Increase 30.55555556 1E+30 475 93.47826087 Allowable Decrease 31.66666667 17.1875 358.3333333 50 = (i) What is the objective function value? Objective Function Value = 50(250) + 237.5(18) + 0(32) + 268.75(15) = 9556.25 units (ii) How much Material used by the optimal solution ? 1800 units (iii) How much time used in Department 1? 150 units (iv) If the Increase in the objective coefficient of Product 1 is 5 units then what happens for the Optimal solution? How about objective function value? 0 (w) If the objective coefficient of Product 4 is decreased by 5 units then what happened for optimal solution? (vi) If there are Simultaneous changes in objective coefficients of Product 2 and Product 3 such that the coefficients of product 2 increases by 2 units and coefficients of product 3 decreases by 7 units then what happened for optimal solution?| (vii) If RHS value of the constraint Time in Department 2 decreases by 20 units then what happens for optimal solution? (viii) If we add a new constraint: P. + P2 2 200 to LP, what happens for optimal solution