How many occupied cells must a transportation matrix with 8 rows and 7 columns have so that it DOES NOT degenerate? 

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HPCL Engineer Mechanical 04 Nov 2022 Official Paper (Shift 2)
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  1. 15
  2. 55
  3. 56
  4. 14

Answer (Detailed Solution Below)

Option 4 : 14
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Detailed Solution

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Concept:-

  • Transportation problem works in the way of minimizing the cost function. The cost function is the amount of money spent on the logistics provider for transporting the commodities from the production or supplier place to the demand place.
  • Transportation deals with the transportation of a commodity (single product) from ‘m’ sources (origin or supply or capacity centers) to ‘n’ destinations (sinks or demand or requirement centers).
  • Non-Degenerate Basic Feasible Solution:-  A basic feasible solution to a (m x n) transportation problem is said to be a non-degenerate basic feasible solution if it contains exactly m+n–1 non-negative allocation in independent positions. 

Calculation:-

Given:-

m = 8, n = 7

The condition of non-degeneracy for the transportation matrix is, No. of occupied cells

⇒ m + n -1

So, No. of occupied cells = 8 + 7 - 1 = 14

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