a$)$ What is the drawback of using graphical method in solving linear programming problems $(2$ marks$)$

b$)$ A firm produces three types of pumps: A$,$ B$,$ C$,$ each of which requires the four processes of turning, drilling assembling and testing. From the information given in the table below, determine

i$.$ the weekly output of each type of pump to maximize profit

ii$.$ the maximum profit

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multirow$[$t$]\{2\}\{*\}\{$Pump type$\}$ & $\backslash$multicolumn$\{4\}\{|$l$|\}\{$Process time $($hour$)$ per pump$\}$ & $\backslash$multirow$[$t$]\{2\}\{*\}\{$Profit per pump $(\backslash$#$)\}\backslash \backslash$

$\backslash$hline & Turning & Drilling & Assembling & Testing & $\backslash \backslash$

$\backslash$hline A & $2$ & $1$ & $3$ & $4$ & $84\backslash \backslash$

$\backslash$hline B & $1$ & $1$ & $4$ & $3$ & $72\backslash \backslash$

$\backslash$hline C & $2$ & $1$ & $2$ & $2$ & $52\backslash \backslash$

$\backslash$hline Total available time $($h$/$week$)$ & $98$ & $60$ & $145$ & $160$ & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$