4. Union City Al has decided to upgrade their tornado warning system. The city leaders have identified six potential locations for erecting a warning siren tower. They want to ensure that each of the seven schools in Union City is within three miles of a siren, yet they want to build as few warning siren towers as possible. Relevant information on the six potential locations of the warning siren towers and distance in miles to each of the seven schools is presented in the table below. Formulate the LP model for Union City to minimize towers built. (10 points)

Potential Locations 
Schools	A	B	C	D	E	F	
1. Washington	2	1	4	8	11	7	
2. Adams	1	2	5	12	9	2
3. Jefferson	4	1	2	5	6	13	
4. Madison 1	5	4	2	6	1
5. Jackson	6	8	2	4	1	7
6. Lincoln	7	4	1	2	6	1
7. Kennedy	9	12	4	1	2	8

5. Kenton owns two fruit stands, one in Montego Bay and one in Kingston. One of Kenton’s most popular products is the guava. Kenton relies on five orchards to provide him with fresh guava each day. The table below summarizes the daily demand at each fruit stand, the daily supply at each orchard, and the cost (per guava delivered to the city of the fruit stand in Jamaican dollars). The supply values in the last row of the table are provided by the orchard. However Kenton knows that the orchards are very unreliable and may not be able to provide as many as claimed on any given day. Therefore, Kenton views the supply figures as the maximum amount possible to obtain from each orchard. He would like to distribute the shipments from the various orchards to the fruit stands to the extent possible. That is, he does not want to rely on one orchard to provide a large portion of the demand to either of the two fruit stands he owns (or put another way, he wants each fruit stand to rely as little as possible on each of the various orchards). The budget for purchasing guavas is limited to 820 Jamaican dollars. Formulate the LP model to ensure daily demand is met within the budget and minimize the number of guava supplied to either fruit stand by any one orchard. 
Fruit Stands Adric Bevaun Carnell Dallan Ervan	Demand
Montego Bay	0.50 0.70	0.60 0.40 0.90 500
Kingston 0.70 0.60 0.50 0.55 0.75 700. 

Supply	150 200 300 100 600

Objective function: ______________________________________________
6. Barnwest Airlines must staff the daily flights between St. Louis and Atlanta as shown in the table below. Barnwest has crews that live in both cities. Each day, a crew must fly one St. Louis to Atlanta flight and one Atlanta to St. Louis flight (the order of the flights for the crew is not important – i.e. which flight is first just depends on where the crew is located and there are plenty of crews in both cities). There must be at least one hour of down time between the two flights. For example, a St. Louis based crew can fly the 9 – 11AM St. Louis to Atlanta flight and return on the noon to 2PM Atlanta to St. Louis flight. This incurs a downtime of one hour between the two fights. They can also return to St Louis on any of the later flights, but the downtime would be longer. Barnwest wants to schedule crews to cover all flights and minimize the total downtime. Formulate LP model. (10 points0

Flight	Leave St. Louis Arrive Atlanta Flight Leave Atlanta Arrive St. Louis
1 6A.M.	8A.M.	1	7A.M. 9A.M.
2 9A.M.	11A.M.	2	8A.M.	10A.M. 
3	NOON	2P.M.	3	10A.M.	NOON
4	3P.M.	5P.M.	4	NOON	2P.M.
5	5P.M.	7P.M.	5	2P.M.	4P.M.
6	7P.M.	9P.M.	6	4P.M.	6P.M.
7	8P.M.	10P.M.	7	7P.M.	9P.M..

Objective function: ______________________________________________