x2+x3 +2x。=20 x2+5x3+x4-x5=20 (2) x1+4x2-x3+x5=10 Now you are to conduct sensitivity analysis by independently investigating each of the following changes in the original model. For each change, use the sensitivity analysis procedure to determine whether the previous optimal solution is till optimal (a) Change the right-hand sides to/6 2 (b)Change the coefficients of x to a,3= 3 2 (c) Introduce a new variable X6 with coefficients a,I (d) Introduce a new constraint 3x,+2x,+3x3 <25 Change constraint 2 to x,+2x2+2x, <35 6. Solve the following parametric linear programming problem (15 points) Maxz()=(10-46)x1+(4-6)x2+(7+0) 3x1+x,+2x3≤7 s2x1+x2+3x1≤5 0 0,x2≥0 when 0=0, the final simplex tableau is Coefficient of Ba asic variabie E X2 X3 X4 5 Right side (0) 0 3 24 7. The BETTER PRODUCTS COMPANY has decided to initiate the production of four new products, using three plants that currently have excess production capacity The products require a comparable production effort per unit, so the availabl production capacity of the plants is measured by the number of units of any product that can be produced per day, as given in the following table. The bottom row gives the required production rate per day to meet projected sales. Each plant can produce any of these products, except that plant 2 cannot produce product 3. However, the variable costs per unit of each product differ from plant to plant. Management now3 (2) 4 10 (1) 5 20 (0) 2 20 1 2 3 5 2 3 4 5 2 3 5 + − + = − + + − = + + + = x x x x x x x x Z x x x Now you are to conduct sensitivity analysis by independently investigating each of the following changes in the original model. For each change, use the sensitivity analysis procedure to determine whether the previous optimal solution is till optimal. (a) Change the right-hand sides to ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 30 20 2 1 b b (b) Change the coefficients of x3 to ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 2 3 2 23 13 3 a a c (c) Introduce a new variable x6 with coefficients ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡− = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 2 1 3 21 11 6 a a c (d) Introduce a new constraint 3x1 + 2x2 + 3x3 ≤ 25 Change constraint 2 to x1 + 2x2 + 2x3 ≤ 35 6. Solve the following parametric linear programming problem (15 points) ⎪ ⎩ ⎪ ⎨ ⎧ ≥ ≥ ≥ + + ≤ + + ≤ = − + − + + 0, 0, 0 2 3 5 3 2 7 . . ( ) (10 4 ) (4 ) (7 ) 1 2 3 1 2 3 1 2 3 1 2 3 x x x x x x x x x st MaxZ θ θ x θ x θ x when θ=0, the final simplex tableau is Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 Right side Z (0) 1 0 0 3 2 2 24 X1 (1) 0 1 0 -1 1 -1 2 X2 (2) 0 0 1 5 -2 3 1 7. The BETTER PRODUCTS COMPANY has decided to initiate the production of four new products, using three plants that currently have excess production capacity. The products require a comparable production effort per unit, so the available production capacity of the plants is measured by the number of units of any product that can be produced per day, as given in the following table. The bottom row gives the required production rate per day to meet projected sales. Each plant can produce any of these products, except that plant 2 cannot produce product 3. However, the variable costs per unit of each product differ from plant to plant. Management now