The tabulation and network diagram below represent a retooling project for a manufacturing company. The retooling is necessary to qualify for funding from a multinational agency for expansion of the plant. The retooling project was originally scheduled for a later date but has to be brought forward and crashed to meet the funding application deadline. $[30]$

a$)$ Find the cost slope, maximum reduced time and the cost for the project for normal time. $[5]$

b$)$ Hence, crash the project to meet a deadline of $18$ days and determine the associated cost. $[20]$

$\backslash$table$[[$Activity$,\backslash$table$[[$Cost$],[$I$.$D$.]],\backslash$table$[[$Maximum$],[$Reduced$]],$Direct Cost$],[,$Normal,Crash,$],[,,,$Time $($d$),$Cost,Time $($d$),$Cost,$],[$A$,,,6,$$$500,4,$$$800,],[$B$,,,3,$$$200,2,$$$400,],[$C$,,,5,$$$500,4,$$$700,],[$D$,,,3,$$$200,1,$$$500,],[$E$,,,2,$$$300,1,$$$600,],[$F$,,,5,$$$400,3,$$$900,],[$G$,,,5,$$$150,4,$$$350,],[$H$,,,8,$$$550,4,$$$1750,]]$