Linear programming: theory and algorithms
What is the solution to the following linear programming problem?
max Z = c1x1 + c2x2 + · · · + cn x n
s.t. a1x1 + a2x2 + · · · + a n x n ≤ b,
0 ≤ x i ≤ u i (i = 1, 2, . . . , n).
Assume that all the data elements (ci , ai , and u i ) are strictly positive and the
coefficients are arranged such that:
c1
a1
≥ c2
a2
≥ · · · ≥ cn
a n
.
Write the problem in standard form and apply the simplex method to it. What will
be the steps of the simplex method when applied to this problem, i.e., in what order
will the variables enter and leave the basis?
