Linear Programming is an important technique in Operations Research.

$($a$)$ List the essential mathematical components of a Linear Programming problem that

can be solved by the simplex method, and common methods of obtaining each of

these mathematical components in practice.

$(8$ marks$)$

$($b$)$ Explain the practical $("$real life"$)$ limitations of each of the mathematical components

listed in your answer to Part $($a$)$ above.

$(8$ marks$)$

$($c$)$ Explain what is commonly referred to as "Sensitivity Analysis" in Linear

Programming. Illustrate your answer by some simple practical examples from

industry.

$(9$ marks$)$