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# Feasibility of a Linear Programming Problem

Exercise 3.22 Consider the following linear programming problem with a single constraint:
minimize &#931; i=1 --> n cixi
subject to = ...
i=1,...,n.

(a) Derive a simple test for checking the feasibility of this problem.

(b) Assuming that the optimal cost is finite, develop a simple method for obtaining an optimal solution directly.

Please see the attached file for the fully formatted problems.

#### Solution Preview

Hi, Here is the question

Minimize Z= c1x1+c2x2+...+cnzn

Subject to

a11 x1+ a12 x2+...+ a1n xn = b1

a21 x1+ a21 x2+...+ a2nxn = b2

......

.......

am1 x1 + am2 x2 + ...+ amn xn = bm

x1,x2,... xn greater than or equal to 0

Where x1,x2...xn are the decision variables

cj (j=1,2,3...n) represents per unit profit or cost to the j-th constraint

bi (i=1,2,3...m) is the requirement or availability of the i-th constraint

aij (i=1,2,3...m ; j= ...

#### Solution Summary

Feasibility is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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