$2.$ The distribution system for the Smith Company consists of three plants $($A$,$ B$,$ and C$),$ two warehouses $($D and E$),$ and four customers $($W$,$ X$,$ Y$,$ and Z$).$ The relevant supply, demand, and unit shipping cost information are given in the table below. Set up and solve the transshipment model to minimize total shipping costs. $($Problem $5-21$ in the textbook$)$

To To

PLANT SUPPLY CUSTOMER DEMAND FROM D E FROM W X Y Z

A $450$ W $450$ A $$4$ $$7$ D $$6$ $$4$ $$8$ $$4$

B $500$ X $300$ B $$8$ $$5$ E $$3$ $$6$ $$7$ $$7$

C $380$ Y $300$ C $$5$ $$6$

Z $400$

$3.$ The Central Police Department has five detective squads available for assignment to five open crime cases. The chief of detective wishes to assign the squads so that the total time to conclude the cases is minimized. The average number of days, based on past performance, for each squad to complete each case is shown in following table. Use the assignment model to find the best solution. $($problem $5-27$ in the textbook$)$

CASE

SQUAD A B C D E

$12773714$

$230612720$

$32154310$

$421127128$

$5826242513$