$7-8$ Develop a model of a cross$-$dock system that groups and transfers material for fur$-$ ther shipment. This facility has five incoming docks and three outgoing docks. Trucks arrive to each of the incoming docks with loads of material on pallets. The interarrival time is UNIF$(30,60)$ between truck arrivals on each incoming dock $($all times are in min$-$ utes$).$ Each truck will have a number of pallets drawn from a UNIF$(10,22)$ distribution $($round to the nearest integer$)$ that need to be transferred to one of the outgoing docks. Assume an equal probability of any incoming pallet going to any of the three outgoing docks. When trucks arrive, an automatic unloading device unloads the pallets at the in$-$ coming dock. Assume that this requires no time, so the pallets are immediately ready for transfer. The pallets are transferred by one of $5$ fork trucks to the outgoing docks, which are located on the other side of the building. The distance between any incoming dock and any outgoing dock is $75$ feet, and the fork trucks travel at $75$ feet per minute. The time for a fork truck to load a pallet is UNIF$(0\mathrm{.}3,0\mathrm{.}4)$ and to unload a pallet is UNIF$(0\mathrm{.}2,0\mathrm{.}4).$ The performance measure of interest is the average time a pallet spends in the sys$-$ tem. $($HINT: If you place all fork trucks at the outgoing docks for their initial position, you don't have to add distances between the incoming docks.$)$ Set the run length to be $720$ minutes and regard this as a terminating simulation. Develop a model for each of the following two cases, and animate your models: $($a$)$ Assume the priority is such that you want to transfer the pallets that have been waiting the longest. $($HINT: Enter the name of the attribute with the arrival time in the priority field of the Transfer Out dialog.$)($b$)$ Because we want to be assured that an incoming truck can always unload, modify your model from part $($a$)$ above such that the pick$-$up priority is placed on the incoming dock with the most pallets. $($HINT: Develop an expression us$-$ ing NQ for the priority field.$)$ Which of the above two options would appear to be "best"? Be sure to justify your conclusions with a valid statistical analysis. Furthermore, for each option, study the effect of having more fork trucks $($up to $7)$; again, be aware of the gap in credibility that results from an inadequate statistical analysis.