The calculations are trivial if the APL functions MACH $\Delta \mathrm{REP}, \mathrm{DWQ} \Delta \mathrm{MR} \Delta \mathrm{C}$, and DW $\Delta \mathrm{MR} \Delta \mathrm{C}$ are available.) The English farnsworth company, Farnsworth Unlimited, Ltd., (a farnsworth is a microelectronic device for gauging the performance of farns) has a number of shops, each of which can be modeled as an $\mathrm{M} / \mathrm{M} / 2 / 3 / 3$ queueing system with $E[O]=10$ minutes and $W_s=8$ minutes. Please do the following:
(a) Calculate $p_i$ for $i=0,1,2,3, q_i$ for $i=0,1,2$, and $W, W_q, L$, and $L_q$ for each system.
(b) Calculate the probability that an inoperative machine must queue for repair.
(c) Calculate $E[q \mid q>0]$.
(d) Calculate $W_q[1]$ and $W[10]$ when time is measured in minutes.