ASSIGNMENT PROBLEM: A technology company has four engineers $($E$1,$ E$2,$ E$3,$ E$4)$ who must be assigned to four projects $($P$1,$ P$2,$ P$3,$ P$4).$ Each engineer has different skill sets and efficiencies for each project, resulting in varying costs for their assignment to those projects. The company aims to minimize the cost of assigning engineers to projects while ensuring that each engineer is assigned to exactly one project and each project is assigned to exactly one engineer. Note the following cost matrix $($in $\backslash$$$)$ associated with each engineer on each project:

a$.$ Provide a linear programming formulation

$[5$ Marks$]$

b$.$ Solve to achieve the company's aim.

$[20$ Marks$]$