Maxz= 2x, +4x +5x x1+3x2+2x3≤5+b sn{x1+2x2+3x3≤6+20 0,x,≥0,x2≥0 where e can be assigned any positive or negative values. Let x4 and xs be the slack variables for the respective functional constraints. After we apply the simplex method with 0=0, the final simplex tableau is Basic variable Coefficient of E XI Right side 0 a. Express the BF solution (and Z) given in this tableau as a function of e Determine the lower and upper bounds on e before this optimal solution would become infeasible Then determine the best choice of 0 between these bound that 0 the bounds found in part(a), determine the allow range to stay optimal for cl(the coefficient of xl in the objective function) 7. Consider the following project network. By using the PErT three-estimate approach, suppose that the usual three estimates for the time required(in weeks) for each of these activities are as follows: (20 points) Activity Optimistic estimate Most likely estimate Pessimistic estimate 2364 14 18 3→6 20 26 26 34 42 6→7 12 (a)On the basis of the estimates just listed, calculate the expected value and standard deviation of the time required for each activity (b)Using expected times, determine the critical path for the project3 ⎪ ⎩ ⎪ ⎨ ⎧ ≥ ≥ ≥ + + ≤ + + + ≤ + = + + 0, 0, 0 2 3 6 2 3 2 5 . . 2 4 5 1 2 3 1 2 3 1 2 3 1 2 3 x x x x x x x x x st MaxZ x x x θ θ where θcan be assigned any positive or negative values. Let x4 and x5 be the slack variables for the respective functional constraints. After we apply the simplex method with θ=0, the final simplex tableau is Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 Right side Z (0) 1 0 1 0 1 1 11 X1 (1) 0 1 5 0 3 -2 3 X3 (2) 0 0 -1 1 -1 1 1 a. Express the BF solution (and Z) given in this tableau as a function ofθ. Determine the lower and upper bounds onθ before this optimal solution would become infeasible. Then determine the best choice of θ between these bounds. b. Given thatθ is between the bounds found in part(a), determine the allowable range to stay optimal for c1(the coefficient of x1 in the objective function). 7. Consider the following project network. By using the PERT three-estimate approach, suppose that the usual three estimates for the time required (in weeks) for each of these activities are as follows:(20 points) Activity Optimistic estimate Most likely estimate Pessimistic estimate 1→2 1→3 2→6 3→4 3→5 3→6 4→5 5→6 5→7 6→7 28 22 26 14 32 40 12 16 26 12 32 28 36 16 32 52 16 20 34 16 36 32 46 18 32 74 24 26 42 30 (a) On the basis of the estimates just listed, calculate the expected value and standard deviation of the time required for each activity. (b) Using expected times, determine the critical path for the project