# In Chapter 2 we solved a two-constraint linear-programming version of a trailer-production…

In Chapter 2 we solved a two-constraint linear-programming version of a trailer-production problem:

Suppose that, in formulating this problem, we ignored a constraint limiting the time available in the shop for inspecting the trailers.

a) If the solution x1 = 36, x2 = 0, and x3 = 6 to the original problem satisfies the inspection constraint, is it necessarily optimal for the problem when we impose the inspection constraint?

b) Suppose that the inspection constraint is x1 + x2 + x3 + x6 = 30, where x6 is a nonnegative slack variable. Add this constraint to the optimal tableau with x6 as its basic variable and pivot to eliminate the basic variables x1 and x3 from this constraint. Is the tableau now in dual canonical form?

c) Use the dual simplex method to find the optimal solution to the trailer-production problem with the inspection constraint given in part (b).

d) Can the ideas used in this example be applied to solve a linear program whenever a new constraint is added after the problem has been solved?

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