For the following LP
Maximize Z = 3x1 + 7x2 + 5x3
subject to:
x1 + x2 + x3 ≤ 50
2x1 + 3x2 + x3 ≤ 100
x1 , x2 , x3 ≥ 0.
The final simplex tableau is given below, where s1 and s2 are the slack variables for constraint 1 and 2. The optimal solution given by this tableau is:
x1 = 0, x2 = 25, x3 = 25, s1 = 0, s2 = 0, Z = 300.
Basic variable | Eq. | Coefficient of: Z x1 x2 x3 s1 s2 | Right Side
Z | (0) | 1 3 0 0 4 1 | 300
x3 | (1) | 0 1/2 0 1 3/2 -1/2 | 25
x2 | (2) | 0 1/2 1 0 -1/2 1/2 | 25
Using the information from the optimal simplex tableau:
a. Determine the range of c1 (coefficient of x1 in the objective function) within which current basis remains optimal.
b. Determine the range of c2 (coefficient of x2 in the objective function) within which current basis remains optimal.
c. Determine the range of b1 (right hand side of the first constraint) within which current basis remains optimal.
d. If the RHS of the first constraint (b1) is changed from 50 to 60, find out the new objective function value for Z from the information given in the optimal simplex tableau (without re-solving).