Consider a four$-$station line with a throughput target of three jobs per hour. Suppose the SCV of amivals to the line is equal to $1\mathrm{.}5.$ Thus, $TH=3$ jobs per hour and $c_a^2=1\mathrm{.}5$ for the first station. Set the target cycle time for the line at $CT=18.$ Assume that only one type of machine is available at each station. $(40$ points$)$

$\backslash$table$[[$Station$,$Number of Machines,$t_e,c_e^2,\backslash$table$[[$Cost $($if$],[$needed$)]]],[1,4,1\mathrm{.}5,1\mathrm{.}5,100],[2,2,0\mathrm{.}78,1,60],[3,\mathrm{.}3,1\mathrm{.}1,2,90],[4,5,1\mathrm{.}6,0\mathrm{.}1,110]]$

a$)$ Calculate the Cycle Time $($CT$)$ for the given plan

b$)$ Is the cycle time greater than $18?$ If so$,$ add machines up until you reach CT of $18$ or less.