3x1+2x,+5 XI x2+x3≤430 s.t. x1+4x2≤420 ≥0 Let x4, Xs and x denote the slack variables for the respective constraints. The final simplex tableau is as follows Basic variable E Coefficient of Right side (1)0 X3 03/20 0 1/2 0 230 2 0-2 (a) Identify the optimal solution from this table (b)Identify the optimal solution for the dual problem (c)Introduce a new constraint x,+2x2+3x3<480, Determine whether the previous optimal solution is till optimal (d) If we want the previous optimal solution to be always optimal, how much does the right-side of constraint 1 b, increase? (e) If a new variable Xnew has been introduced into the model, Xnew coefficient is 27 324 Determine whether the previous optimal solution is till optimal 7. Solve the parameter programming as follow: (15 points) Max==2x,+x2 x1s10+20 x1+x2≤25-0 x,<10+26 x1≥0,x2≥0 8. At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor(purchase price minus trade-in allowance, plus running and maintenance costsO at the end of year I and3 ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≥ + ≤ + ≤ + + ≤ = + + 0 4 420 3 2 460 2 430 3 2 5 1 2 3 1 2 1 3 1 2 3 1 2 3 x x x x x x x x x x x x x , , s.t max z Let x4,x5, and x6 denote the slack variables for the respective constraints. The final simplex tableau is as follows: Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 X6 Right side Z (0) 1 4 0 0 1 2 0 X2 (1) 0 -1/4 1 0 1/2 -1/4 0 100 X3 (2) 0 3/2 0 1 0 1/2 0 230 X6 (3) 0 2 0 0 -2 1 1 20 (a) Identify the optimal solution from this table. (b) Identify the optimal solution for the dual problem. (c) Introduce a new constraint 480 x1 + 2x2 + 3x3 ≤ , Determine whether the previous optimal solution is till optimal. (d) If we want the previous optimal solution to be always optimal, how much does the right-side of constraint 1 b1 increase? . (e) If a new variable Xnew has been introduced into the model, Xnew coefficient is ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ 4 2 3 9 37 27 17 7 a a a c . Determine whether the previous optimal solution is till optimal. 7.Solve the parameter programming as follow: (15 points) ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≥ ≥ ≤ + + ≤ − ≤ + = + 0, 0 10 2 25 10 2 . . 2 1 2 2 1 2 1 1 2 x x x x x x st Maxz x x θ θ θ 8. At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs0 at the end of year I and