Consider the following problem.

Maximize Z 9x1  8x2  5x3, subject to 2x1  3x2  x3 4 5x1  4x2  3x3 11 and x1  0, x2  0, x3  0.

Let x4 and x5 denote the slack variables for the respective functional constraints. After we apply the simplex method, the final simplex tableau is D,I

(a) Suppose that a new technology has become available for conducting the first activity considered in this problem. If the new technology were adopted to replace the existing one, the coefficients of x1 in the model would change from to .

Use the sensitivity analysis procedure to investigate the potential effect and desirability of adopting the new technology. Specifically, assuming it were adopted, construct the resulting revised final tableau, convert this tableau to proper form from Gaussian elimination, and then reoptimize (if necessary) to find the new optimal solution.

(b) Now suppose that you have the option of mixing the old and new technologies for conducting the first activity. Let  denote the fraction of the technology used that is from the new tech-

nology, so 0  1. Given , the coefficients of x1 in the model become

.

Construct the resulting revised final tableau (as a function of

), and convert this tableau to proper form from Gaussian elimination. Use this tableau to identify the current basic solution as a function of . Over the allowable values of 0  1, give the range of values of  for which this solution is both feasible and optimal. What is the best choice of  within this range?