The state of Missouri has three major power-generating companies identified as 1, 2, and 3. During the months of peak demand, the Missouri Power Authority authorizes these companies to pool their excess capacity and to produce and distribute electricity to smaller independent power companies that do not have generators large enough to handle all the demand. The supply, up to the excess capacity, is distributed on the basis of cost per kilowatt-hour transmitted.

The table below contains the costs (in cents) per kilowatt-hour (kwh) of transmitting power from the major companies 1, 2, and 3 to each of four different small companies W, X, Y, and Z. Also shown in the table are the demand and capacity for power in millions of kilowatt-hours (Mkwh).

FROM	W	X	Y	Z	Excess Capacity (Mkwh)
1	12 cents	4 cents	9 cents	5 cents	45
2	8 cents	1 cent	6 cents	7 cents	55
3	1 cent	12 cents	4 cents	6 cents	50
Unfilled Demand (Mkwh)	40	20	50	20

The problem is to determine the best way to allocate the power, in millions of kilowatt-hours, from the major companies to the small independents so as to keep the total distribution costs to the lowest that is possible.

(NOTE: Unit costs in the table above are listed in units of cents/kwh. Capacity and demand are both in units of Mkwh. HINT: In your modeling, convert the unit costs to either cents/Mkwh or $/Mkwh.)

Please just convert these units to $/Mkwh

1- What special kind of LP problem is this?

2- Is this problem balanced or unbalanced? If it is unbalanced, which way is it unbalanced and by how much?

3- define the decision variables. Be explicit and specific(including units)

4- In terms of the decision variables you defined in part 3, state mathematecally the objective function.

5- in terms of the decision variables you defined in part 3, state mathematically all the constraints of the situation described.

6- Is the problem you formulated mathematically in part 3 and 5, inclusive, a linear program or not? if it is explain why.

7- solve this problem with a computer using Lingo.

8- On the basis of your computer solution in part 7, what routes between company and small independent are used?

9- on the basis of your computer solution 7, how much electric power is sent over each and every one of this routes?what is the total electric power is sent all over these routes?

10-on the basis of computer solution 7, what is the total dollar cost of this allocation of electricity?

11- Is there any slack in this solution? if yes where is the slack, what does this slack represent and how much is the slack?

12- draw the final network representation of this problem showing only the routes that are used.

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