7. Solve the parameter programming as follow:(15 points) Maxz= 2x, +x 10+26 x1+x2≤25-6 x2≤10+26 x1≥0,x2≥0 Solution: when 0=0, the optimal tableau is Basic variable Eq Coe d2000 Right side 0 X4 (2) 0000 When the right-side is b= 25-0 the final tableau is 10+26 Coefficient of asic varia (3 X4X5Right side 000 0 30+60 (1) 000 0 0 10+20 (2) 5-50 10+26 So, when<e<l, the optimal solution is x1=10+2 0, x2=10+2 0, maxZ=30+60 When<0<5. the final tableau is Basic variable Eq Coefficient of XI X3 4 X5Right side 0 0 000 l1l1 0 0 10+20 0 0 5-5 0 15-36 When1<0s5 the final tableau is Basic variable Coefficient of E X4 Right side 000 000 0 (2) 0 20+10 X3 30-15 When> 25, the problem has no optimal solution 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 be5 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 Solution: when θ=0, the optimal tableau is Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 Right side Z (0) 1 0 0 2 0 1 30 X1 (1) 0 1 0 1 0 0 10 X4 (2) 0 0 0 -1 1 -1 5 X2 (3) 0 0 1 0 0 1 10 When the right-side is ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ + − + = θ θ θ 10 2 25 10 2 b ,the final tableau is Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 Right side Z (0) 1 0 0 2 0 1 30+6θ X1 (1) 0 1 0 1 0 0 10+2θ X4 (2) 0 0 0 -1 1 -1 5-5θ X2 (3) 0 0 1 0 0 1 10+2θ So, when0<θ≤1,the optimal solution is x1=10+2θ,x2=10+2θ,maxZ=30+6θ When1 < θ ≤ 5 , the final tableau is Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 Right side Z (0) 1 0 0 1 1 0 35+θ X1 (1) 0 1 0 1 0 0 10+2θ X5 (2) 0 0 0 1 -1 1 5θ-5 X2 (3) 0 0 1 -1 1 0 15-3θ When1 < θ ≤ 5 , the final tableau is Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 Right side Z (0) 1 0 1 0 2 0 50-2θ X1 (1) 0 1 1 0 1 0 25-θ X5 (2) 0 0 1 0 0 1 2θ+10 X3 (3) 0 0 -1 1 -1 0 3θ-15 Whenθ ≥ 25 , the problem has no optimal solution. 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