The following table shows the sensitivity analysis for a LP problem. Adjustable Cells Cell Name $B$10 No. of Units Product 1 $C$10 No. of Units Product 2 $D$10 No. of Units Product 3 $E$10 No. of Units Product 4 Final Reduced Value Cost 500 237. 5 0 0 -4.375 268. 75 0 Objective Allowable Coefficient Increase 13.625 18 4.5 324 .375 15 6.6 Allowable Decrease 1 E+30 5.5 1E+30 2.058823529 Constraints Final Cell Name Value $B$16 Department 1 time LHS 150 $B$17 Department 2 time LHS102.8125 $B$18 Material LHS 1800 $B$19 Min production level LHS 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 (i) What is the objective function value? (ii) How much Material used by the optimal solution? (iii) How much time used in Department 1? (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? (v) 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 + P22 200 to LP, what happens for optimal solution