The initial simplex tableau on page M7-49 was developed by Tommy Gibbs, vice president of a large cotton spinning mill. Unfortunately, Gibbs quit before completing this important LP application. Stephanie Robbins, the newly hired replacement, was immediately given the task of using LP to determine what different kinds of yarn the mill should use to minimize costs. Her first need was to be certain that Gibbs correctly formulated the objective function and constraints. She could find no statement of the problem in the files, so she decided to reconstruct the problem from the initial tableau.

(a) What is the correct formulation, using real decision variables (that is, Xi’s) only?

(b) Which variable will enter this current solution mix in the second tableau? Which basic variable willleave?

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$12 S18 $10 $20 $8 0 SO SO $0 $0 M M M M SOLUTION MIx S, S S, S, Ss A1 A2 A, A QUANTITY SM A 100 25 0 10-1 0 0 00 0 0 250 150 25 0 000 0 0 00300 18 -15 15 0 M A 0 0 0 00- 001 -S14M -S5M S5M $21M SM SO S0-SM $0-SM SM SM SM SM $570M C,-Z 12 21M 18+14M 10+5M 20 5M 7-21M 8-M0 0 M M00 00