Now use a software package based on the simplex method to generate sensitivity analysis information preparatory to doing parts

(a) and

(c) below.

C

(a) Suppose that the estimates for c1 and c2 are correct but the estimates for both b1 and b2 are incorrect. Consider the following four cases where the true values of b1 and b2 differ from their estimates by the same percentage: (1) both b1 and b2 are smaller than their estimates, (2) both b1 and b2 are larger than their estimates, (3) b1 is smaller and b2 is larger than their estimates, and (4) b1 is larger and b2 is smaller than their estimates. For each of these cases, use the 100 percent rule for simultaneous changes in right-hand sides to determine how large the percentage error can be while guaranteeing that the original shadow prices still will be valid.

(b) For each of the four cases considered in part (a), start with the final simplex tableau given in Prob. 6.7-21 and use algebraic analysis based on the fundamental insight presented in Sec. 5.3 to determine how large the percentage error can be without invalidating the original shadow prices.

C

(c) Suppose that the estimates for b1 and b2 are correct but the estimates for both c1 and c2 are incorrect. Consider the following four cases where the true values of c1 and c2 differ from their estimates by the same percentage: (1) both c1 and c2 are smaller than their estimates, (2) both c1 and c2 are larger than their estimates, (3) c1 is smaller and c2 is larger than their estimates, and (4) c1 is larger and c2 is smaller than their estimates. For each of these cases, use the 100 percent rule for simultaneous changes in objective function coefficients to determine how large the percentage error can be while guaranteeing that the original optimal solution must still be optimal.

(d) For each of the four cases considered in part (c), start with the final simplex tableau given in Prob. 6.7-21 and use algebraic analysis based on the fundamental insight presented in Sec. 5.3 to determine how large the percentage error can be without invalidating the original optimal solution.