Minimizing shipping costs by vogel-s approximation method

Question

1) Describe the scope of Operations Research in detail.

2) Explain the models used in Operation Research.

3) Resolve the Linear Programming problem given below by using Big Method.

                 Minimize Z = 10X₁+15X₂+20X₃
Subject to               2X₁+4X₂+6X₃≥ 24
                               3X₁+9X₂+6X₃≥ 30
                                       X₁, X₂, X₃≥ 0             
4) Explain Transportation problem. Write down a method of determining the initial feasible solution.

5) Company having plants at P, Q and R supplies to warehouses at W, X, Y and Z.  Monthly plant capacities are 75, 95 and 120 respectively.  Monthly warehouse requirements are 55, 65, 75 and 100 respectively.  Unit shipping costs are as follows.

   W    X   Y    Z
P 18   21  15  12
Q 16   22  26  15
R 16   15  16  17

Find out the optimum distribution for this company to minimize shipping costs using Vogel’s Approximation method for initial solution.

6) Write down the name of the types of models of Inventory system and describe them in detail.