Question:-
Consider the following linear programming problem :
Max. z = 2A + 3B, subject to A + B £ 10,
4A + 6B £ 30, 2A + B £ 17, A, B, ³ 0
What can one say about the solution ?
Option (A)
It may contain alternative optima
Option (B)
The solution will be unbounded
Option(C)
The solution will be degenerate
Option(D)
It cannot be solved by simplex method
Correct Option:
(A)
Question Solution:
Z = 2A + 3B
A + B £ 10
(A/10) + (B/10) £ 1
4A + 6B £ 30
(A/7.5) + (B/5) £ 1
2A + B £ 17
(A/8.5) + (B/17) £ 1
A, B £ 0

Z(7.5, 0) = 15
Z(0, 5) = 15
Maximum value of objective function = 15 and it has alternative optimal solutions because of same constraint as objective function.
question-answer-faq-8713