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Linear Prog COP4355_Part_13

# Linear Prog COP4355_Part_13 - 56 4.18 Chapter 4 Linear...

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56 Chapter 4 Linear Programming: The Simplex Algorithm 4.18 a. - < C 1 | Z 1 |; so - < C 1 23 No change in optimum solution, since X 1 is nonbasic. b. Since X 2 is a basic variable, we compute 2 2j Z a for each nonbasic variable. These values (-15, and +9, ignoring the artificial variables) tell us the amounts by which C 2 can change before bringing a new variable into the solution. -15 C 2 +9, or -10 C 2 +14 is the allowable range. If C 2 is reduced, Z OPT is reduced, if C 2 is increased, so is Z OPT . c. S 1 b 1 < + ; so -8.167 b 1 < + , but since b i cannot be negative, 0 b 1 < + is the range. The only change is -1 for 1 reduction of S 1 if b 1 is reduced and a similar increase in S 1 as b 1 is increased. d. Constraint #2 is binding, so the limits on the allowable change in b 2 are found by computing i i2 -X a . The positive a i2 values determine the lower bound and the negative a i2 values determine the upper bound.

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