Question

2) Given the constraint below:

7T – 8W + 3K + 100 = -800 – K – T

a) Convert the constraint into a Standard Form:

b)What is the basic variable associated with the Standard Form constraint above?

c)Convert the constraint into Tableau form:

d)What is the basic variable associated with the Tableau Form constraint?

e)Write the objective function of the LP in a general form, which has n variables and m equations.

Answer 1

a)

In standard form, variables are on the left hand side and constants on the right hand side. Resulting equation is:

(7T - 8W + 3K) - (-K - T) = -800 - 100

8T - 8W + 4K = -900

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b)

Basic variable associated with the standard form is T, W, K

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c)

Tableau form is following:

		T	W	K	a1
-M	a1	8	-8	4	-1	-900

where, M is a hypothetical large number

and a1 is auxiliary constraint, having a negligibly small value.

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d)

Basic variable associated with the tableau form constraint is either slack/surplus or auxiliary variable.

In this case, there is no slack or suplus variable. So, auxiliary variable, a1, is the basic variable of initial tableau.

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e)

Generalized form of objective function of LP is:

Maximize Z = CijXij, where i={1,2,..n}, and j={1,2,..m}