Case Study On Linear Programming

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      The mathematical models which tells to optimise (minimize or maximise) the objective function Z subject to certain condition on the variables is called a Linear programming problem (LPP).       
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The standard form of the linear programming problem is used to develop the procedure for solving a general programming problem. A general LPP is of the form Max (or min) Z = c1x1 + c2x2 + ͙ +cnxn x1, x2, ....xn are called decision variable.

     
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The Application Areas of Linear Programming are: 1. Transportation Problem 2. Military Applications 3. Operation of System Of Dams 4. Personnel Assignment Problem 5. Other Applications: (a). manufacturing plants, (b). distribution centres, (c). production management and manpower management.

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   c
 State Board is planning to build new plant for ten years. 

   

  
      
½ coal energy ½ Hydroelectric power with no reservoirs ½ Hydroelectric power with small reservoirs(to meet daily fluctuations) ½ Hydroelectric power with Large reservoirs(to meet seasonal fluctuations) c
   !   ½ Total Annual Usage ½ Peak usage Of Power ½ Guaranteed Power Output Unit Of capacity-to produce 1 billion killowatt hour per year

characteristics Of Annual Plant !

"        #  

       #  

$ %
  
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&&&

Steam

0.15

.20

1200

2600

Hydroelectric Without reservoir

0.10

.10

1600

1680

Hydroelectric With small reservoir

0.10

.40

2400

2560

Hydroelectric With large reservoir

0.80

.90

4000

4400

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1) Help the company in developing a 10 year plan that would detail how many capacity of each type of plant to be build.

2) Develop a LP model and solve it to minimize the total discount cost. however there is a restriction that no more than Rs. 140000 million can be used for investment in plant over the ten years.

 

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